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import java.io.OutputStream;
import java.io.OutputStream;
import java.io.IOException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStream;
/**
/**
* Built using CHelper plug-in
* Built using CHelper plug-in
* Actual solution is at the top
* Actual solution is at the top
*/
*/
public class Main {
public class Main {
public static void main(String[] args) {
public static void main(String[] args) {
InputStream inputStream = System.in;
InputStream inputStream = System.in;
OutputStream outputStream = System.out;
OutputStream outputStream = System.out;
InputReader in = new InputReader(inputStream);
InputReader in = new InputReader(inputStream);
OutputWriter out = new OutputWriter(outputStream);
OutputWriter out = new OutputWriter(outputStream);
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ConnectedPermutations
solver = new
ConnectedPermutations
();
ColoredForests
solver = new
ColoredForests
();
solver.solve(1, in, out);
solver.solve(1, in, out);
out.close();
out.close();
}
}
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static class
ConnectedPermutations
{
static class
ColoredForests
{
public static int mod = 924844033;
public static int mod = 924844033;
public static long pr = Utils.mod_exp(5, 21 * 21 * 2, mod);
public static long pr = Utils.mod_exp(5, 21 * 21 * 2, mod);
public static long[] om;
public static long[] om;
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public static long[] cways;
public long[] fact;
public long[] ifact;
public long[] inv;
public long[] vals;
public long[] vals;
public long[] tr;
public long[] tr;
static {
static {
om = new long[21];
om = new long[21];
om[20] = pr;
om[20] = pr;
for (int i = 19; i >= 0; i--) {
for (int i = 19; i >= 0; i--) {
om[i] = om[i + 1] * om[i + 1] % mod;
om[i] = om[i + 1] * om[i + 1] % mod;
}
}
}
}
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public long comb(int n, int k) {
return fact[n] * ifact[k] % mod * ifact[n - k] % mod;
}
public void solve(int testNumber, InputReader in, OutputWriter out) {
public void solve(int testNumber, InputReader in, OutputWriter out) {
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int n = in.nextInt()
;
int n = in.nextInt()
, c = in.nextInt()
;
int m = 1 <<
19;
int m = 1 <<
17;
cways = new long[m + 2];
cways[0] = 1;
long[][] x = Factorials.getFIF(m + 2, mod);
fact = x[0];
ifact = x[1];
inv = x[2];
for (int i = 0; i < c; i++) cways[i] = 0;
long[][] pow = new long[c + 1][cways.length];
for (int i = 1; i <= c; i++) {
pow[i][0] = 1;
for (int j = 1; j < cways.length; j++) {
pow[i][j] = pow[i][j - 1] * i % mod;
}
}
long[][] comb = new long[c + 1][c + 1];
for (int i = 0; i <= c; i++) for (int j = 0; j <= i; j++) comb[i][j] = comb(i, j);
for (int i = c; i < cways.length; i++) {
cways[i] = Utils.mod_exp(c, i, mod);
for (int j = i - 1; j >= i - c; j--) {
if (((i - j) & 1) == 1) {
cways[i] = (cways[i] - comb[c][c - i + j] * pow[c - i + j][i]) % mod;
if (cways[i] < 0) cways[i] += mod;
} else {
cways[i] = (cways[i] + comb[c][c - i + j] * pow[c - i + j][i]) % mod;
}
}
}
vals = new long[m + 1];
vals = new long[m + 1];
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vals[1] = 1;
for (int i = 2; i <= m; i++) vals[i] = vals[i - 1] * i % mod;
tr = new long[m + 1];
tr = new long[m + 1];
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System.arraycopy(
vals
, 0, tr, 0, m + 1)
;
for (int i = 1; i <= m; i++) {
f(
1
, m
);
tr[i] = Utils.mod_exp(i, i - 2, mod) * ifact[i - 1] % mod * cways[i] % mod;
}
vals
[0] = 1
;
f(
0
, m
- 1
);
for (int i = 1; i <= n; i++)
for (int i = 1; i <= n; i++)
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out.println(vals[i]
);
out.println(vals[i]
* fact[i] % mod
);
}
}
public void f(int start, int end) {
public void f(int start, int end) {
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if (start == end)
return;
if (start == end)
{
if (start != 0) vals[start] = vals[start] * inv[start] % mod;
return;
}
int mid = (start + end) / 2;
int mid = (start + end) / 2;
f(start, mid);
f(start, mid);
long[] x = Arrays.copyOfRange(vals, start, mid + 1);
long[] x = Arrays.copyOfRange(vals, start, mid + 1);
long[] rr = multiply(x, tr);
long[] rr = multiply(x, tr);
for (int i = mid + 1; i <= end; i++)
for (int i = mid + 1; i <= end; i++)
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vals[i] = (vals[i]
-
rr[i - start] + mod) % mod;
vals[i] = (vals[i]
+
rr[i - start] + mod) % mod;
f(mid + 1, end);
f(mid + 1, end);
}
}
public void fft(long[] a, long omega) {
public void fft(long[] a, long omega) {
int N = a.length;
int N = a.length;
if (N == 1) return;
if (N == 1) return;
long[] even = new long[N / 2];
long[] even = new long[N / 2];
long[] odd = new long[N / 2];
long[] odd = new long[N / 2];
for (int i = 0; 2 * i < N; i++) even[i] = a[2 * i];
for (int i = 0; 2 * i < N; i++) even[i] = a[2 * i];
for (int i = 0; 2 * i + 1 < N; i++) odd[i] = a[2 * i + 1];
for (int i = 0; 2 * i + 1 < N; i++) odd[i] = a[2 * i + 1];
long omega2 = omega * omega % mod;
long omega2 = omega * omega % mod;
fft(even, omega2);
fft(even, omega2);
fft(odd, omega2);
fft(odd, omega2);
long cur = 1;
long cur = 1;
for (int i = 0; i < N / 2; i++) {
for (int i = 0; i < N / 2; i++) {
long x = cur * odd[i] % mod;
long x = cur * odd[i] % mod;
a[i] = (even[i] + x) % mod;
a[i] = (even[i] + x) % mod;
a[i + N / 2] = (even[i] + mod - x) % mod;
a[i + N / 2] = (even[i] + mod - x) % mod;
cur = cur * omega % mod;
cur = cur * omega % mod;
}
}
}
}
public long[] multiply(long[] a, long[] b) {
public long[] multiply(long[] a, long[] b) {
int resultSize = Integer.highestOneBit(a.length - 1) << 2;
int resultSize = Integer.highestOneBit(a.length - 1) << 2;
resultSize = Math.max(resultSize, 2);
resultSize = Math.max(resultSize, 2);
long[] ax = new long[resultSize];
long[] ax = new long[resultSize];
long[] bx = new long[resultSize];
long[] bx = new long[resultSize];
for (int i = 0; i < a.length; i++)
for (int i = 0; i < a.length; i++)
ax[i] = a[i];
ax[i] = a[i];
for (int i = 0; i < b.length && i < resultSize; i++)
for (int i = 0; i < b.length && i < resultSize; i++)
bx[i] = b[i];
bx[i] = b[i];
int ww = 31 - Integer.numberOfLeadingZeros(resultSize);
int ww = 31 - Integer.numberOfLeadingZeros(resultSize);
fft(ax, om[ww]);
fft(ax, om[ww]);
fft(bx, om[ww]);
fft(bx, om[ww]);
for (int i = 0; i < resultSize; i++)
for (int i = 0; i < resultSize; i++)
ax[i] = ax[i] * bx[i] % mod;
ax[i] = ax[i] * bx[i] % mod;
fft(ax, Utils.inv(om[ww], mod));
fft(ax, Utils.inv(om[ww], mod));
long[] result = new long[resultSize];
long[] result = new long[resultSize];
long d = Utils.inv(resultSize, mod);
long d = Utils.inv(resultSize, mod);
for (int i = 0; i < resultSize; i++) {
for (int i = 0; i < resultSize; i++) {
result[i] = ax[i] * d % mod;
result[i] = ax[i] * d % mod;
}
}
return result;
return result;
}
}
}
}
static class OutputWriter {
static class OutputWriter {
private final PrintWriter writer;
private final PrintWriter writer;
public OutputWriter(OutputStream outputStream) {
public OutputWriter(OutputStream outputStream) {
writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
}
}
public OutputWriter(Writer writer) {
public OutputWriter(Writer writer) {
this.writer = new PrintWriter(writer);
this.writer = new PrintWriter(writer);
}
}
public void close() {
public void close() {
writer.close();
writer.close();
}
}
public void println(long i) {
public void println(long i) {
writer.println(i);
writer.println(i);
}
}
}
}
static class InputReader {
static class InputReader {
private InputStream stream;
private InputStream stream;
private byte[] buf = new byte[1024];
private byte[] buf = new byte[1024];
private int curChar;
private int curChar;
private int numChars;
private int numChars;
public InputReader(InputStream stream) {
public InputReader(InputStream stream) {
this.stream = stream;
this.stream = stream;
}
}
public int read() {
public int read() {
if (this.numChars == -1) {
if (this.numChars == -1) {
throw new InputMismatchException();
throw new InputMismatchException();
} else {
} else {
if (this.curChar >= this.numChars) {
if (this.curChar >= this.numChars) {
this.curChar = 0;
this.curChar = 0;
try {
try {
this.numChars = this.stream.read(this.buf);
this.numChars = this.stream.read(this.buf);
} catch (IOException var2) {
} catch (IOException var2) {
throw new InputMismatchException();
throw new InputMismatchException();
}
}
if (this.numChars <= 0) {
if (this.numChars <= 0) {
return -1;
return -1;
}
}
}
}
return this.buf[this.curChar++];
return this.buf[this.curChar++];
}
}
}
}
public int nextInt() {
public int nextInt() {
int c;
int c;
for (c = this.read(); isSpaceChar(c); c = this.read()) {
for (c = this.read(); isSpaceChar(c); c = this.read()) {
;
;
}
}
byte sgn = 1;
byte sgn = 1;
if (c == 45) {
if (c == 45) {
sgn = -1;
sgn = -1;
c = this.read();
c = this.read();
}
}
int res = 0;
int res = 0;
while (c >= 48 && c <= 57) {
while (c >= 48 && c <= 57) {
res *= 10;
res *= 10;
res += c - 48;
res += c - 48;
c = this.read();
c = this.read();
if (isSpaceChar(c)) {
if (isSpaceChar(c)) {
return res * sgn;
return res * sgn;
}
}
}
}
throw new InputMismatchException();
throw new InputMismatchException();
}
}
public static boolean isSpaceChar(int c) {
public static boolean isSpaceChar(int c) {
return c == 32 || c == 10 || c == 13 || c == 9 || c == -1;
return c == 32 || c == 10 || c == 13 || c == 9 || c == -1;
}
}
}
}
static class Utils {
static class Utils {
public static long inv(long N, long M) {
public static long inv(long N, long M) {
long x = 0, lastx = 1, y = 1, lasty = 0, q, t, a = N, b = M;
long x = 0, lastx = 1, y = 1, lasty = 0, q, t, a = N, b = M;
while (b != 0) {
while (b != 0) {
q = a / b;
q = a / b;
t = a % b;
t = a % b;
a = b;
a = b;
b = t;
b = t;
t = x;
t = x;
x = lastx - q * x;
x = lastx - q * x;
lastx = t;
lastx = t;
t = y;
t = y;
y = lasty - q * y;
y = lasty - q * y;
lasty = t;
lasty = t;
}
}
return (lastx + M) % M;
return (lastx + M) % M;
}
}
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public static long mod_exp(long b, long e, long mod) {
long res = 1;
while (e > 0) {
if ((e & 1) == 1)
res = (res * b) % mod;
b = (b * b) % mod;
e >>= 1;
}
return res;
}
}
static class Factorials {
public static long[][] getFIF(int max, int mod) {
long[] fact = new long[max];
long[] ifact = new long[max];
long[] inv = new long[max];
inv[1] = 1;
for (int i = 2; i < max; i++) {
inv[i] = (mod - mod / i) * inv[mod % i] % mod;
}
fact[0] = 1;
ifact[0] = 1;
for (int i = 1; i < max; i++) {
fact[i] = fact[i - 1] * i % mod;
ifact[i] = ifact[i - 1] * inv[i] % mod;
}
return new long[][]{fact, ifact, inv};
}
}
}
}
}
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import java.io.OutputStream; import java.io.IOException; import java.io.InputStream; import java.io.OutputStream; import java.io.PrintWriter; import java.util.Arrays; import java.io.BufferedWriter; import java.io.Writer; import java.io.OutputStreamWriter; import java.util.InputMismatchException; import java.io.IOException; import java.io.InputStream; /** * Built using CHelper plug-in * Actual solution is at the top */ public class Main { public static void main(String[] args) { InputStream inputStream = System.in; OutputStream outputStream = System.out; InputReader in = new InputReader(inputStream); OutputWriter out = new OutputWriter(outputStream); ConnectedPermutations solver = new ConnectedPermutations(); solver.solve(1, in, out); out.close(); } static class ConnectedPermutations { public static int mod = 924844033; public static long pr = Utils.mod_exp(5, 21 * 21 * 2, mod); public static long[] om; public long[] vals; public long[] tr; static { om = new long[21]; om[20] = pr; for (int i = 19; i >= 0; i--) { om[i] = om[i + 1] * om[i + 1] % mod; } } public void solve(int testNumber, InputReader in, OutputWriter out) { int n = in.nextInt(); int m = 1 << 19; vals = new long[m + 1]; vals[1] = 1; for (int i = 2; i <= m; i++) vals[i] = vals[i - 1] * i % mod; tr = new long[m + 1]; System.arraycopy(vals, 0, tr, 0, m + 1); f(1, m); for (int i = 1; i <= n; i++) out.println(vals[i]); } public void f(int start, int end) { if (start == end) return; int mid = (start + end) / 2; f(start, mid); long[] x = Arrays.copyOfRange(vals, start, mid + 1); long[] rr = multiply(x, tr); for (int i = mid + 1; i <= end; i++) vals[i] = (vals[i] - rr[i - start] + mod) % mod; f(mid + 1, end); } public void fft(long[] a, long omega) { int N = a.length; if (N == 1) return; long[] even = new long[N / 2]; long[] odd = new long[N / 2]; for (int i = 0; 2 * i < N; i++) even[i] = a[2 * i]; for (int i = 0; 2 * i + 1 < N; i++) odd[i] = a[2 * i + 1]; long omega2 = omega * omega % mod; fft(even, omega2); fft(odd, omega2); long cur = 1; for (int i = 0; i < N / 2; i++) { long x = cur * odd[i] % mod; a[i] = (even[i] + x) % mod; a[i + N / 2] = (even[i] + mod - x) % mod; cur = cur * omega % mod; } } public long[] multiply(long[] a, long[] b) { int resultSize = Integer.highestOneBit(a.length - 1) << 2; resultSize = Math.max(resultSize, 2); long[] ax = new long[resultSize]; long[] bx = new long[resultSize]; for (int i = 0; i < a.length; i++) ax[i] = a[i]; for (int i = 0; i < b.length && i < resultSize; i++) bx[i] = b[i]; int ww = 31 - Integer.numberOfLeadingZeros(resultSize); fft(ax, om[ww]); fft(bx, om[ww]); for (int i = 0; i < resultSize; i++) ax[i] = ax[i] * bx[i] % mod; fft(ax, Utils.inv(om[ww], mod)); long[] result = new long[resultSize]; long d = Utils.inv(resultSize, mod); for (int i = 0; i < resultSize; i++) { result[i] = ax[i] * d % mod; } return result; } } static class OutputWriter { private final PrintWriter writer; public OutputWriter(OutputStream outputStream) { writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream))); } public OutputWriter(Writer writer) { this.writer = new PrintWriter(writer); } public void close() { writer.close(); } public void println(long i) { writer.println(i); } } static class InputReader { private InputStream stream; private byte[] buf = new byte[1024]; private int curChar; private int numChars; public InputReader(InputStream stream) { this.stream = stream; } public int read() { if (this.numChars == -1) { throw new InputMismatchException(); } else { if (this.curChar >= this.numChars) { this.curChar = 0; try { this.numChars = this.stream.read(this.buf); } catch (IOException var2) { throw new InputMismatchException(); } if (this.numChars <= 0) { return -1; } } return this.buf[this.curChar++]; } } public int nextInt() { int c; for (c = this.read(); isSpaceChar(c); c = this.read()) { ; } byte sgn = 1; if (c == 45) { sgn = -1; c = this.read(); } int res = 0; while (c >= 48 && c <= 57) { res *= 10; res += c - 48; c = this.read(); if (isSpaceChar(c)) { return res * sgn; } } throw new InputMismatchException(); } public static boolean isSpaceChar(int c) { return c == 32 || c == 10 || c == 13 || c == 9 || c == -1; } } static class Utils { public static long inv(long N, long M) { long x = 0, lastx = 1, y = 1, lasty = 0, q, t, a = N, b = M; while (b != 0) { q = a / b; t = a % b; a = b; b = t; t = x; x = lastx - q * x; lastx = t; t = y; y = lasty - q * y; lasty = t; } return (lastx + M) % M; } } }
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import java.io.OutputStream; import java.io.IOException; import java.io.InputStream; import java.io.OutputStream; import java.io.PrintWriter; import java.util.Arrays; import java.io.BufferedWriter; import java.io.Writer; import java.io.OutputStreamWriter; import java.util.InputMismatchException; import java.io.IOException; import java.io.InputStream; /** * Built using CHelper plug-in * Actual solution is at the top */ public class Main { public static void main(String[] args) { InputStream inputStream = System.in; OutputStream outputStream = System.out; InputReader in = new InputReader(inputStream); OutputWriter out = new OutputWriter(outputStream); ColoredForests solver = new ColoredForests(); solver.solve(1, in, out); out.close(); } static class ColoredForests { public static int mod = 924844033; public static long pr = Utils.mod_exp(5, 21 * 21 * 2, mod); public static long[] om; public static long[] cways; public long[] fact; public long[] ifact; public long[] inv; public long[] vals; public long[] tr; static { om = new long[21]; om[20] = pr; for (int i = 19; i >= 0; i--) { om[i] = om[i + 1] * om[i + 1] % mod; } } public long comb(int n, int k) { return fact[n] * ifact[k] % mod * ifact[n - k] % mod; } public void solve(int testNumber, InputReader in, OutputWriter out) { int n = in.nextInt(), c = in.nextInt(); int m = 1 << 17; cways = new long[m + 2]; cways[0] = 1; long[][] x = Factorials.getFIF(m + 2, mod); fact = x[0]; ifact = x[1]; inv = x[2]; for (int i = 0; i < c; i++) cways[i] = 0; long[][] pow = new long[c + 1][cways.length]; for (int i = 1; i <= c; i++) { pow[i][0] = 1; for (int j = 1; j < cways.length; j++) { pow[i][j] = pow[i][j - 1] * i % mod; } } long[][] comb = new long[c + 1][c + 1]; for (int i = 0; i <= c; i++) for (int j = 0; j <= i; j++) comb[i][j] = comb(i, j); for (int i = c; i < cways.length; i++) { cways[i] = Utils.mod_exp(c, i, mod); for (int j = i - 1; j >= i - c; j--) { if (((i - j) & 1) == 1) { cways[i] = (cways[i] - comb[c][c - i + j] * pow[c - i + j][i]) % mod; if (cways[i] < 0) cways[i] += mod; } else { cways[i] = (cways[i] + comb[c][c - i + j] * pow[c - i + j][i]) % mod; } } } vals = new long[m + 1]; tr = new long[m + 1]; for (int i = 1; i <= m; i++) { tr[i] = Utils.mod_exp(i, i - 2, mod) * ifact[i - 1] % mod * cways[i] % mod; } vals[0] = 1; f(0, m - 1); for (int i = 1; i <= n; i++) out.println(vals[i] * fact[i] % mod); } public void f(int start, int end) { if (start == end) { if (start != 0) vals[start] = vals[start] * inv[start] % mod; return; } int mid = (start + end) / 2; f(start, mid); long[] x = Arrays.copyOfRange(vals, start, mid + 1); long[] rr = multiply(x, tr); for (int i = mid + 1; i <= end; i++) vals[i] = (vals[i] + rr[i - start] + mod) % mod; f(mid + 1, end); } public void fft(long[] a, long omega) { int N = a.length; if (N == 1) return; long[] even = new long[N / 2]; long[] odd = new long[N / 2]; for (int i = 0; 2 * i < N; i++) even[i] = a[2 * i]; for (int i = 0; 2 * i + 1 < N; i++) odd[i] = a[2 * i + 1]; long omega2 = omega * omega % mod; fft(even, omega2); fft(odd, omega2); long cur = 1; for (int i = 0; i < N / 2; i++) { long x = cur * odd[i] % mod; a[i] = (even[i] + x) % mod; a[i + N / 2] = (even[i] + mod - x) % mod; cur = cur * omega % mod; } } public long[] multiply(long[] a, long[] b) { int resultSize = Integer.highestOneBit(a.length - 1) << 2; resultSize = Math.max(resultSize, 2); long[] ax = new long[resultSize]; long[] bx = new long[resultSize]; for (int i = 0; i < a.length; i++) ax[i] = a[i]; for (int i = 0; i < b.length && i < resultSize; i++) bx[i] = b[i]; int ww = 31 - Integer.numberOfLeadingZeros(resultSize); fft(ax, om[ww]); fft(bx, om[ww]); for (int i = 0; i < resultSize; i++) ax[i] = ax[i] * bx[i] % mod; fft(ax, Utils.inv(om[ww], mod)); long[] result = new long[resultSize]; long d = Utils.inv(resultSize, mod); for (int i = 0; i < resultSize; i++) { result[i] = ax[i] * d % mod; } return result; } } static class OutputWriter { private final PrintWriter writer; public OutputWriter(OutputStream outputStream) { writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream))); } public OutputWriter(Writer writer) { this.writer = new PrintWriter(writer); } public void close() { writer.close(); } public void println(long i) { writer.println(i); } } static class InputReader { private InputStream stream; private byte[] buf = new byte[1024]; private int curChar; private int numChars; public InputReader(InputStream stream) { this.stream = stream; } public int read() { if (this.numChars == -1) { throw new InputMismatchException(); } else { if (this.curChar >= this.numChars) { this.curChar = 0; try { this.numChars = this.stream.read(this.buf); } catch (IOException var2) { throw new InputMismatchException(); } if (this.numChars <= 0) { return -1; } } return this.buf[this.curChar++]; } } public int nextInt() { int c; for (c = this.read(); isSpaceChar(c); c = this.read()) { ; } byte sgn = 1; if (c == 45) { sgn = -1; c = this.read(); } int res = 0; while (c >= 48 && c <= 57) { res *= 10; res += c - 48; c = this.read(); if (isSpaceChar(c)) { return res * sgn; } } throw new InputMismatchException(); } public static boolean isSpaceChar(int c) { return c == 32 || c == 10 || c == 13 || c == 9 || c == -1; } } static class Utils { public static long inv(long N, long M) { long x = 0, lastx = 1, y = 1, lasty = 0, q, t, a = N, b = M; while (b != 0) { q = a / b; t = a % b; a = b; b = t; t = x; x = lastx - q * x; lastx = t; t = y; y = lasty - q * y; lasty = t; } return (lastx + M) % M; } public static long mod_exp(long b, long e, long mod) { long res = 1; while (e > 0) { if ((e & 1) == 1) res = (res * b) % mod; b = (b * b) % mod; e >>= 1; } return res; } } static class Factorials { public static long[][] getFIF(int max, int mod) { long[] fact = new long[max]; long[] ifact = new long[max]; long[] inv = new long[max]; inv[1] = 1; for (int i = 2; i < max; i++) { inv[i] = (mod - mod / i) * inv[mod % i] % mod; } fact[0] = 1; ifact[0] = 1; for (int i = 1; i < max; i++) { fact[i] = fact[i - 1] * i % mod; ifact[i] = ifact[i - 1] * inv[i] % mod; } return new long[][]{fact, ifact, inv}; } } }
Trouver la différence