結果
| 問題 | No.42 貯金箱の溜息 |
| ユーザー |
 suisen
|
| 提出日時 | 2021-03-27 12:46:56 |
| 言語 | Java21 (openjdk 21) |
| 結果 |
RE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 26,666 bytes |
| コンパイル時間 | 4,135 ms |
| コンパイル使用メモリ | 98,716 KB |
| 実行使用メモリ | 37,272 KB |
| 最終ジャッジ日時 | 2024-05-06 21:55:09 |
| 合計ジャッジ時間 | 4,515 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | RE | - |
| testcase_01 | RE | - |
| testcase_02 | RE | - |
ソースコード
import java.io.EOFException;
import java.io.File;
import java.io.FileDescriptor;
import java.io.FileInputStream;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.UncheckedIOException;
import java.lang.reflect.Field;
import java.nio.CharBuffer;
import java.nio.charset.CharacterCodingException;
import java.nio.charset.CharsetEncoder;
import java.nio.charset.StandardCharsets;
import java.util.Arrays;
import java.util.OptionalLong;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
public class Main {
public static void main(String[] args) throws Exception {
ExtendedScanner sc = new ExtendedScanner();
FastPrintStream pw = new FastPrintStream();
solve(sc, pw);
sc.close();
pw.flush();
pw.close();
}
static final class ModArithmetic1000000009 extends ModArithmetic {
public static final ModArithmetic INSTANCE = new ModArithmetic1000000009();
private ModArithmetic1000000009(){}
public static final long MOD = 1000000009;
public long getMod() {return MOD;}
public long mod(long a) {return (a %= MOD) < 0 ? a + MOD : a;}
public long add(long a, long b) {return (a += b) >= MOD ? a - MOD : a;}
public long sub(long a, long b) {return (a -= b) < 0 ? a + MOD : a;}
public long mul(long a, long b) {return (a * b) % MOD;}
}
static final ModArithmetic ma = ModArithmetic1000000009.INSTANCE;
static final int MAX = 3000;
static final int D = 500;
static final int[] C = new int[]{1, 5, 10, 50, 100, 500};
public static void solve(ExtendedScanner sc, FastPrintStream pw) {
int t = sc.nextInt();
long[] dp = new long[MAX];
dp[0] = 1;
for (int c : C) {
for (int i = c; i < MAX; i++) {
dp[i] = ma.add(dp[i], dp[i - c]);
}
}
long[][] ys = new long[D][MAX / D];
for (int i = 0; i < MAX; i++) {
ys[i % D][i / D] = dp[i];
}
while (t --> 0) {
long m = sc.nextLong();
pw.println(LagrangeInterpolation.lagrangeInterpolation(ys[(int) (m % D)], m / D, ma));
}
}
}
/**
* @author https://atcoder.jp/users/suisen
*/
final class ExtendedScanner extends FastScanner {
public ExtendedScanner() {super();}
public ExtendedScanner(InputStream in) {super(in);}
public int[] ints(final int n) {
final int[] a = new int[n];
Arrays.setAll(a, $ -> nextInt());
return a;
}
public int[] ints(final int n, final IntUnaryOperator f) {
final int[] a = new int[n];
Arrays.setAll(a, $ -> f.applyAsInt(nextInt()));
return a;
}
public int[][] ints(final int n, final int m) {
final int[][] a = new int[n][];
Arrays.setAll(a, $ -> ints(m));
return a;
}
public int[][] ints(final int n, final int m, final IntUnaryOperator f) {
final int[][] a = new int[n][];
Arrays.setAll(a, $ -> ints(m, f));
return a;
}
public long[] longs(final int n) {
final long[] a = new long[n];
Arrays.setAll(a, $ -> nextLong());
return a;
}
public long[] longs(final int n, final LongUnaryOperator f) {
final long[] a = new long[n];
Arrays.setAll(a, $ -> f.applyAsLong(nextLong()));
return a;
}
public long[][] longs(final int n, final int m) {
final long[][] a = new long[n][];
Arrays.setAll(a, $ -> longs(m));
return a;
}
public long[][] longs(final int n, final int m, final LongUnaryOperator f) {
final long[][] a = new long[n][];
Arrays.setAll(a, $ -> longs(m, f));
return a;
}
public char[][] charArrays(final int n) {
final char[][] c = new char[n][];
Arrays.setAll(c, $ -> nextChars());
return c;
}
public double[] doubles(final int n) {
final double[] a = new double[n];
Arrays.setAll(a, $ -> nextDouble());
return a;
}
public double[][] doubles(final int n, final int m) {
final double[][] a = new double[n][];
Arrays.setAll(a, $ -> doubles(m));
return a;
}
public String[] strings(final int n) {
final String[] s = new String[n];
Arrays.setAll(s, $ -> next());
return s;
}
}
/**
* @author https://atcoder.jp/users/suisen
*/
class FastPrintStream implements AutoCloseable {
private static final int INT_MAX_LEN = 11;
private static final int LONG_MAX_LEN = 20;
private int precision = 9;
private static final int BUF_SIZE = 1 << 14;
private static final int BUF_SIZE_MINUS_INT_MAX_LEN = BUF_SIZE - INT_MAX_LEN;
private static final int BUF_SIZE_MINUS_LONG_MAX_LEN = BUF_SIZE - LONG_MAX_LEN;
private final byte[] buf = new byte[BUF_SIZE];
private int ptr = 0;
private final Field strField;
private final CharsetEncoder encoder;
private final OutputStream out;
public FastPrintStream(OutputStream out) {
this.out = out;
Field f;
try {
f = String.class.getDeclaredField("value");
f.setAccessible(true);
} catch (NoSuchFieldException | SecurityException e) {
f = null;
}
this.strField = f;
this.encoder = StandardCharsets.US_ASCII.newEncoder();
}
public FastPrintStream(File file) throws IOException {
this(new FileOutputStream(file));
}
public FastPrintStream(String filename) throws IOException {
this(new File(filename));
}
public FastPrintStream() {
this(new FileOutputStream(FileDescriptor.out));
}
public FastPrintStream println() {
if (ptr == BUF_SIZE) internalFlush();
buf[ptr++] = (byte) '\n';
return this;
}
public FastPrintStream println(Object o) {
return print(o).println();
}
public FastPrintStream println(String s) {
return print(s).println();
}
public FastPrintStream println(char[] s) {
return print(s).println();
}
public FastPrintStream println(char c) {
return print(c).println();
}
public FastPrintStream println(int x) {
return print(x).println();
}
public FastPrintStream println(long x) {
return print(x).println();
}
public FastPrintStream println(double d, int precision) {
return print(d, precision).println();
}
public FastPrintStream println(double d) {
return print(d).println();
}
private FastPrintStream print(byte[] bytes) {
int n = bytes.length;
if (ptr + n > BUF_SIZE) {
internalFlush();
try {
out.write(bytes);
} catch (IOException e) {
throw new UncheckedIOException(e);
}
} else {
System.arraycopy(bytes, 0, buf, ptr, n);
ptr += n;
}
return this;
}
public FastPrintStream print(Object o) {
return print(o.toString());
}
public FastPrintStream print(String s) {
if (strField == null) {
return print(s.getBytes());
} else {
try {
Object value = strField.get(s);
if (value instanceof byte[]) {
return print((byte[]) value);
} else {
return print((char[]) value);
}
} catch (IllegalAccessException e) {
return print(s.getBytes());
}
}
}
public FastPrintStream print(char[] s) {
try {
return print(encoder.encode(CharBuffer.wrap(s)).array());
} catch (CharacterCodingException e) {
byte[] bytes = new byte[s.length];
for (int i = 0; i < s.length; i++) {
bytes[i] = (byte) s[i];
}
return print(bytes);
}
}
public FastPrintStream print(char c) {
if (ptr == BUF_SIZE) internalFlush();
buf[ptr++] = (byte) c;
return this;
}
public FastPrintStream print(int x) {
if (ptr > BUF_SIZE_MINUS_INT_MAX_LEN) internalFlush();
if (-10 < x && x < 10) {
if (x < 0) {
buf[ptr++] = '-';
x = -x;
}
buf[ptr++] = (byte) ('0' + x);
return this;
}
int d;
if (x < 0) {
if (x == Integer.MIN_VALUE) {
buf[ptr++] = '-'; buf[ptr++] = '2'; buf[ptr++] = '1'; buf[ptr++] = '4';
buf[ptr++] = '7'; buf[ptr++] = '4'; buf[ptr++] = '8'; buf[ptr++] = '3';
buf[ptr++] = '6'; buf[ptr++] = '4'; buf[ptr++] = '8';
return this;
}
d = len(x = -x);
buf[ptr++] = '-';
} else {
d = len(x);
}
int j = ptr += d;
while (x > 0) {
buf[--j] = (byte) ('0' + (x % 10));
x /= 10;
}
return this;
}
public FastPrintStream print(long x) {
if ((int) x == x) return print((int) x);
if (ptr > BUF_SIZE_MINUS_LONG_MAX_LEN) internalFlush();
int d;
if (x < 0) {
if (x == Long.MIN_VALUE) {
buf[ptr++] = '-'; buf[ptr++] = '9'; buf[ptr++] = '2'; buf[ptr++] = '2';
buf[ptr++] = '3'; buf[ptr++] = '3'; buf[ptr++] = '7'; buf[ptr++] = '2';
buf[ptr++] = '0'; buf[ptr++] = '3'; buf[ptr++] = '6'; buf[ptr++] = '8';
buf[ptr++] = '5'; buf[ptr++] = '4'; buf[ptr++] = '7'; buf[ptr++] = '7';
buf[ptr++] = '5'; buf[ptr++] = '8'; buf[ptr++] = '0'; buf[ptr++] = '8';
return this;
}
d = len(x = -x);
buf[ptr++] = '-';
} else {
d = len(x);
}
int j = ptr += d;
while (x > 0) {
buf[--j] = (byte) ('0' + (x % 10));
x /= 10;
}
return this;
}
public FastPrintStream print(double d, int precision) {
if (d < 0) {
print('-');
d = -d;
}
d += Math.pow(10, -precision) / 2;
print((long) d).print('.');
d -= (long) d;
for(int i = 0; i < precision; i++){
d *= 10;
print((int) d);
d -= (int) d;
}
return this;
}
public FastPrintStream print(double d) {
return print(d, precision);
}
public void setPrecision(int precision) {
this.precision = precision;
}
private void internalFlush() {
try {
out.write(buf, 0, ptr);
ptr = 0;
} catch (IOException e) {
throw new UncheckedIOException(e);
}
}
public void flush() {
try {
out.write(buf, 0, ptr);
out.flush();
ptr = 0;
} catch (IOException e) {
throw new UncheckedIOException(e);
}
}
public void close() {
try {
out.close();
} catch (IOException e) {
throw new UncheckedIOException(e);
}
}
private static int len(int x) {
return
x >= 1000000000 ? 10 :
x >= 100000000 ? 9 :
x >= 10000000 ? 8 :
x >= 1000000 ? 7 :
x >= 100000 ? 6 :
x >= 10000 ? 5 :
x >= 1000 ? 4 :
x >= 100 ? 3 :
x >= 10 ? 2 : 1;
}
private static int len(long x) {
return
x >= 1000000000000000000L ? 19 :
x >= 100000000000000000L ? 18 :
x >= 10000000000000000L ? 17 :
x >= 1000000000000000L ? 16 :
x >= 100000000000000L ? 15 :
x >= 10000000000000L ? 14 :
x >= 1000000000000L ? 13 :
x >= 100000000000L ? 12 :
x >= 10000000000L ? 11 : 10;
}
}
/**
* @author https://atcoder.jp/users/suisen
*/
class FastScanner implements AutoCloseable {
private final ByteBuffer tokenBuf = new ByteBuffer();
public final InputStream in;
private final byte[] rawBuf = new byte[1 << 14];
private int ptr = 0;
private int buflen = 0;
public FastScanner(InputStream in) {
this.in = in;
}
public FastScanner() {
this(new FileInputStream(FileDescriptor.in));
}
private int readByte() {
if (ptr < buflen) return rawBuf[ptr++];
ptr = 0;
try {
buflen = in.read(rawBuf);
if (buflen > 0) {
return rawBuf[ptr++];
} else {
throw new EOFException();
}
} catch (IOException e) {
throw new UncheckedIOException(e);
}
}
private int readByteUnsafe() {
if (ptr < buflen) return rawBuf[ptr++];
ptr = 0;
try {
buflen = in.read(rawBuf);
if (buflen > 0) {
return rawBuf[ptr++];
} else {
return -1;
}
} catch (IOException e) {
throw new UncheckedIOException(e);
}
}
private int skipUnprintableChars() {
int b = readByte();
while (b <= 32 || b >= 127) b = readByte();
return b;
}
private void loadToken() {
tokenBuf.clear();
for (int b = skipUnprintableChars(); 32 < b && b < 127; b = readByteUnsafe()) {
tokenBuf.append(b);
}
}
public final boolean hasNext() {
for (int b = readByteUnsafe(); b <= 32 || b >= 127; b = readByteUnsafe()) {
if (b == -1) return false;
}
--ptr;
return true;
}
public final String next() {
loadToken();
return new String(tokenBuf.getRawBuf(), 0, tokenBuf.size());
}
public final String nextLine() {
tokenBuf.clear();
for (int b = readByte(); b != '\n'; b = readByteUnsafe()) {
if (b == -1) break;
tokenBuf.append(b);
}
return new String(tokenBuf.getRawBuf(), 0, tokenBuf.size());
}
public final char nextChar() {
return (char) skipUnprintableChars();
}
public final char[] nextChars() {
loadToken();
return tokenBuf.toCharArray();
}
public final long nextLong() {
long n = 0;
boolean isNegative = false;
int b = skipUnprintableChars();
if (b == '-') {
isNegative = true;
b = readByteUnsafe();
}
if (b < '0' || '9' < b) throw new NumberFormatException();
while ('0' <= b && b <= '9') {
// -9223372036854775808 - 9223372036854775807
if (n >= 922337203685477580L) {
if (n > 922337203685477580L) {
throw new ArithmeticException("long overflow");
}
if (isNegative) {
if (b >= '9') {
throw new ArithmeticException("long overflow");
}
n = -n - (b - '0');
} else {
if (b >= '8') {
throw new ArithmeticException("long overflow");
}
n = n * 10 + b - '0';
}
b = readByteUnsafe();
if ('0' <= b && b <= '9') {
throw new ArithmeticException("long overflow");
} else if (b <= 32 || b >= 127) {
return n;
} else {
throw new NumberFormatException();
}
}
n = n * 10 + b - '0';
b = readByteUnsafe();
}
if (b <= 32 || b >= 127) return isNegative ? -n : n;
throw new NumberFormatException();
}
public final int nextInt() {
long value = nextLong();
if ((int) value != value) {
throw new ArithmeticException("int overflow");
}
return (int) value;
}
public final double nextDouble() {
return Double.parseDouble(next());
}
public final void close() {
try {
in.close();
} catch (IOException e) {
throw new UncheckedIOException(e);
}
}
@SuppressWarnings("UnusedReturnValue")
private static final class ByteBuffer {
private static final int DEFAULT_BUF_SIZE = 1 << 12;
private byte[] buf;
private int ptr = 0;
private ByteBuffer(@SuppressWarnings("SameParameterValue") int capacity) {
this.buf = new byte[capacity];
}
private ByteBuffer() {
this(DEFAULT_BUF_SIZE);
}
private ByteBuffer append(int b) {
if (ptr == buf.length) {
int newLength = buf.length << 1;
byte[] newBuf = new byte[newLength];
System.arraycopy(buf, 0, newBuf, 0, buf.length);
buf = newBuf;
}
buf[ptr++] = (byte) b;
return this;
}
private char[] toCharArray() {
char[] chs = new char[ptr];
for (int i = 0; i < ptr; i++) {
chs[i] = (char) buf[i];
}
return chs;
}
private byte[] getRawBuf() {
return buf;
}
private int size() {
return ptr;
}
private void clear() {
ptr = 0;
}
}
}
class LagrangeInterpolation {
public static long lagrangeInterpolation(long[] y, long t, ModArithmetic MA) {
int n = y.length - 1;
t = MA.mod(t);
if (0 <= t && t <= n) {
return MA.mod(y[(int) t]);
}
long ret = 0;
long[] l = new long[n + 1];
long[] r = new long[n + 1];
l[0] = r[n] = 1;
for (int i = 0; i < n; i++) {
l[i + 1] = MA.mul(l[i], t - i);
}
for (int i = n; i > 0; i--) {
r[i - 1] = MA.mul(r[i], t - i);
}
long[] ifac = MA.factorialInv(n);
for (int i = 0; i <= n; i++) {
long v = MA.mul(MA.mod(y[i]), ifac[i], ifac[n - i], l[i], r[i]);
if (((n - i) & 1) == 0) {
ret += v;
} else {
ret -= v;
}
}
return MA.mod(ret);
}
}
/**
* @author https://atcoder.jp/users/suisen
*/
abstract class ModArithmetic {
public abstract long getMod();
public abstract long mod(long a);
public abstract long add(long a, long b);
public abstract long sub(long a, long b);
public abstract long mul(long a, long b);
public final long div(long a, long b) {return mul(a, inv(b));}
public final long inv(long a) {
a = mod(a);
long b = getMod();
long u = 1, v = 0;
while (b >= 1) {
long t = a / b;
a -= t * b;
long tmp1 = a; a = b; b = tmp1;
u -= t * v;
long tmp2 = u; u = v; v = tmp2;
}
if (a != 1) throw new ArithmeticException("divide by zero");
return mod(u);
}
public final long fma(long a, long b, long c) {return add(mul(a, b), c);}
public final long pow(long a, long b) {
long pow = 1;
for (a = mod(a); b > 0; b >>= 1, a = mul(a, a)) {
if ((b & 1) == 1) pow = mul(pow, a);
}
return pow;
}
public final long add(long a, long b, long c) {return mod(a + b + c);}
public final long add(long a, long b, long c, long d) {return mod(a + b + c + d);}
public final long add(long a, long b, long c, long d, long e) {return mod(a + b + c + d + e);}
public final long add(long a, long b, long c, long d, long e, long f) {return mod(a + b + c + d + e + f);}
public final long add(long a, long b, long c, long d, long e, long f, long g) {return mod(a + b + c + d + e + f + g);}
public final long add(long a, long b, long c, long d, long e, long f, long g, long h) {return mod(a + b + c + d + e + f + g + h);}
public final long add(long... xs) {long s = 0; for (long x : xs) s += x; return mod(s);}
public final long mul(long a, long b, long c) {return mul(a, mul(b, c));}
public final long mul(long a, long b, long c, long d) {return mul(a, mul(b, mul(c, d)));}
public final long mul(long a, long b, long c, long d, long e) {return mul(a, mul(b, mul(c, mul(d, e))));}
public final long mul(long a, long b, long c, long d, long e, long f) {return mul(a, mul(b, mul(c, mul(d, mul(e, f)))));}
public final long mul(long a, long b, long c, long d, long e, long f, long g) {return mul(a, mul(b, mul(c, mul(d, mul(e, mul(f, g))))));}
public final long mul(long a, long b, long c, long d, long e, long f, long g, long h) {return mul(a, mul(b, mul(c, mul(d, mul(e, mul(f, mul(g, h)))))));}
public final long mul(long... xs) {long s = 1; for (long x : xs) s = mul(s, x); return s;}
/**
* @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
*/
public final long[] gcdInv(long a) {
final long m = getMod();
a = mod(a);
if (a == 0) return new long[]{m, 0};
long s = m, t = a;
long m0 = 0, m1 = 1;
while (t > 0) {
long u = s / t;
s -= t * u;
m0 -= m1 * u;
long tmp;
tmp = s; s = t; t = tmp;
tmp = m0; m0 = m1; m1 = tmp;
}
if (m0 < 0) m0 += m / s;
return new long[]{s, m0};
}
public final OptionalLong sqrt(long a) {
a = mod(a);
if (a == 0) return OptionalLong.of(0);
if (a == 1) return OptionalLong.of(1);
long p = getMod();
if (pow(a, (p - 1) >> 1) != 1) {
return OptionalLong.empty();
}
if ((p & 3) == 3) {
return OptionalLong.of(pow(a, (p + 1) >> 2));
}
if ((p & 7) == 5) {
if (pow(a, (p - 1) >> 2) == 1) {
return OptionalLong.of(pow(a, (p + 3) >> 3));
} else {
return OptionalLong.of(mul(pow(2, (p - 1) >> 2), pow(a, (p + 3) >> 3)));
}
}
long S = 0, Q = p - 1;
while ((Q & 1) == 0) {
++S;
Q >>= 1;
}
long z = 1;
while (pow(z, (p - 1) >> 1) != p - 1) ++z;
long c = pow(z, Q), R = pow(a, (Q + 1) / 2), t = pow(a, Q), M = S;
while (t != 1) {
long cur = t;
int i;
for (i = 1; i < M; i++) {
cur = mul(cur, cur);
if (cur == 1) break;
}
long b = pow(c, 1L << (M - i - 1));
c = mul(b, b); R = mul(R, b); t = mul(t, b, b); M = i;
}
return OptionalLong.of(R);
}
public final int primitiveRoot() {
final int m = Math.toIntExact(getMod());
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int[] divs = new int[20];
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long) i * i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) x /= i;
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2; ; g++) {
boolean ok = true;
for (int i = 0; i < cnt; i++) {
if (pow(g, (m - 1) / divs[i]) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
/** array operations */
public final long[] rangeInv(int n) {
final long MOD = getMod();
long[] invs = new long[n + 1];
if (n == 0) return invs;
invs[1] = 1;
for (int i = 2; i <= n; i++) {
invs[i] = mul(MOD - MOD / i, invs[(int) (MOD % i)]);
}
return invs;
}
public final long[] arrayInv(long[] a) {
int n = a.length;
long[] l = new long[n + 1];
long[] r = new long[n + 1];
l[0] = r[n] = 1;
for (int i = 0; i < n; i++) l[i + 1] = mul(l[i], a[i ]);
for (int i = n; i > 0; i--) r[i - 1] = mul(r[i], a[i - 1]);
long invAll = inv(l[n]);
long[] invs = new long[n];
for (int i = 0; i < n; i++) {
invs[i] = mul(l[i], r[i + 1], invAll);
}
return invs;
}
public final long[] factorial(int n) {
long[] ret = new long[n + 1];
ret[0] = 1;
for (int i = 1; i <= n; i++) ret[i] = mul(ret[i - 1], i);
return ret;
}
public final long[] factorialInv(int n) {
long facN = 1;
for (int i = 2; i <= n; i++) facN = mul(facN, i);
long[] invs = new long[n + 1];
invs[n] = inv(facN);
for (int i = n; i > 0; i--) invs[i - 1] = mul(invs[i], i);
return invs;
}
public final long[] rangePower(long a, int n) {
a = mod(a);
long[] pows = new long[n + 1];
pows[0] = 1;
for (int i = 1; i <= n; i++) pows[i] = mul(pows[i - 1], a);
return pows;
}
public final long[] rangePowerInv(long a, int n) {
a = mod(a);
long[] invs = new long[n + 1];
invs[n] = inv(pow(a, n));
for (int i = n; i > 0; i--) invs[i - 1] = mul(invs[i], a);
return invs;
}
/** combinatric operations */
public final long[][] combTable(int n) {
long[][] comb = new long[n + 1][];
for (int i = 0; i <= n; i++) {
comb[i] = new long[i + 1];
comb[i][0] = comb[i][i] = 1;
for (int j = 1; j < i; j++) {
comb[i][j] = add(comb[i - 1][j - 1], comb[i - 1][j]);
}
}
return comb;
}
public final long naiveComb(long n, int r) {
if (r < 0 || r > n) return 0;
long num = 1, den = 1;
for (int i = 0; i < r; i++) {
num = mul(num, mod(n - i));
den = mul(den, i + 1);
}
return div(num, den);
}
public final long naivePerm(long n, long r) {
if (r < 0 || r > n) return 0;
long res = 1;
for (long i = 0; i < r; i++) res = mul(res, n - i);
return res;
}
public final long naiveFactorial(int n) {
return naivePerm(n, n);
}
}