結果
| 問題 |
No.109 N! mod M
|
| ユーザー |
 uwi
|
| 提出日時 | 2015-01-16 23:49:11 |
| 言語 | Java (openjdk 23) |
| 結果 |
AC
|
| 実行時間 | 255 ms / 5,000 ms |
| コード長 | 6,514 bytes |
| コンパイル時間 | 2,177 ms |
| コンパイル使用メモリ | 86,224 KB |
| 実行使用メモリ | 53,076 KB |
| 最終ジャッジ日時 | 2024-06-22 04:49:43 |
| 合計ジャッジ時間 | 3,845 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 9 |
ソースコード
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
public class Main {
static InputStream is;
static PrintWriter out;
static String INPUT = "";
static void solve()
{
int[] primes = sieveEratosthenes(100000);
for(int T = ni();T >= 1;T--){
int n = ni(), m = ni();
if(n <= 500000){
long ret = 1 % m;
for(int i = 1;i <= n;i++){
ret = ret * i % m;
}
out.println(ret);
}else{
int[][] f = factor(m, primes);
long div = 1, res = 0;
for(int[] fp : f){
long lres = ff(n, fp[0], fp[1]);
long lmul = 1;
for(int i = 0;i < fp[1];i++)lmul *= fp[0];
res = crt(lmul, lres, div, res);
div *= lmul;
}
out.println(res);
}
}
}
static long ff(int n, int p, int e)
{
if(n >= (long)p*e)return 0;
if(e >= 2)throw new RuntimeException();
long ret = p-1;
long mul = 1;
for(int i = p-1;i >= n+1;i--){
mul = mul * i % p;
}
ret = ret * invl(mul, p) % p;
return ret;
}
public static long invl(long a, long mod) {
long b = mod;
long p = 1, q = 0;
while (b > 0) {
long c = a / b;
long d;
d = a;
a = b;
b = d % b;
d = p;
p = q;
q = d - c * q;
}
return p < 0 ? p + mod : p;
}
public static long[] exgcd(long a, long b)
{
if(a == 0 || b == 0)return null;
int as = Long.signum(a);
int bs = Long.signum(b);
a = Math.abs(a); b = Math.abs(b);
long p = 1, q = 0, r = 0, s = 1;
while(b > 0){
long c = a / b;
long d;
d = a; a = b; b = d % b;
d = p; p = q; q = d - c * q;
d = r; r = s; s = d - c * s;
}
return new long[]{a, p * as, r * bs};
}
public static long crt(long p, long m, long q, long n)
{
long[] apr = exgcd(p, q);
if((n - m) % apr[0] != 0)return -1;
long mod = p * (q / apr[0]);
long a = (apr[1] * ((n - m) / apr[0]) * p + m) % mod;
if(a < 0)a += mod;
return a;
}
public static int[][] factor(int n, int[] primes)
{
int[][] ret = new int[9][2];
int rp = 0;
for(int p : primes){
if(p * p > n)break;
int i;
for(i = 0;n % p == 0;n /= p, i++);
if(i > 0){
ret[rp][0] = p;
ret[rp][1] = i;
rp++;
}
}
if(n != 1){
ret[rp][0] = n;
ret[rp][1] = 1;
rp++;
}
return Arrays.copyOf(ret, rp);
}
public static int[] sieveEratosthenes(int n)
{
if(n <= 32){
int[] primes = {2,3,5,7,11,13,17,19,23,29,31};
for(int i = 0;i < primes.length;i++){
if(n < primes[i]){
return Arrays.copyOf(primes, i);
}
}
return primes;
}
int u = n+32;
double lu = Math.log(u);
int[] ret = new int[(int)(u/lu+u/lu/lu*1.5)];
ret[0] = 2;
int pos = 1;
int[] isnp = new int[(n+1)/32/2+1];
int sup = (n+1)/32/2+1;
int[] tprimes = {3,5,7,11,13,17,19,23,29,31};
for(int tp : tprimes){
ret[pos++] = tp;
int[] ptn = new int[tp];
for(int i = (tp-3)/2;i < tp<<5;i+=tp)ptn[i>>5] |= 1<<i;
for(int j = 0;j < sup;j += tp){
for(int i = 0;i < tp && i+j < sup;i++){
isnp[j+i] |= ptn[i];
}
}
}
// 3,5,7
// 2x+3=n
int[] magic = {0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4, 13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17, 9, 6, 16, 5, 15, 14};
int h = n/2;
for(int i = 0;i < sup;i++){
for(int j = ~isnp[i];j != 0;j &= j-1){
int pp = i<<5|magic[(j&-j)*0x076be629>>>27];
int p = 2*pp+3;
if(p > n)break;
ret[pos++] = p;
if((long)p*p > n)continue;
for(int q = (p*p-3)/2;q <= h;q += p)isnp[q>>5] |= 1<<q;
}
}
return Arrays.copyOf(ret, pos);
}
public static void main(String[] args) throws Exception
{
long S = System.currentTimeMillis();
is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
out = new PrintWriter(System.out);
solve();
out.flush();
long G = System.currentTimeMillis();
tr(G-S+"ms");
}
private static boolean eof()
{
if(lenbuf == -1)return true;
int lptr = ptrbuf;
while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
try {
is.mark(1000);
while(true){
int b = is.read();
if(b == -1){
is.reset();
return true;
}else if(!isSpaceChar(b)){
is.reset();
return false;
}
}
} catch (IOException e) {
return true;
}
}
private static byte[] inbuf = new byte[1024];
static int lenbuf = 0, ptrbuf = 0;
private static int readByte()
{
if(lenbuf == -1)throw new InputMismatchException();
if(ptrbuf >= lenbuf){
ptrbuf = 0;
try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
if(lenbuf <= 0)return -1;
}
return inbuf[ptrbuf++];
}
private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
private static double nd() { return Double.parseDouble(ns()); }
private static char nc() { return (char)skip(); }
private static String ns()
{
int b = skip();
StringBuilder sb = new StringBuilder();
while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
sb.appendCodePoint(b);
b = readByte();
}
return sb.toString();
}
private static char[] ns(int n)
{
char[] buf = new char[n];
int b = skip(), p = 0;
while(p < n && !(isSpaceChar(b))){
buf[p++] = (char)b;
b = readByte();
}
return n == p ? buf : Arrays.copyOf(buf, p);
}
private static char[][] nm(int n, int m)
{
char[][] map = new char[n][];
for(int i = 0;i < n;i++)map[i] = ns(m);
return map;
}
private static int[] na(int n)
{
int[] a = new int[n];
for(int i = 0;i < n;i++)a[i] = ni();
return a;
}
private static int ni()
{
int num = 0, b;
boolean minus = false;
while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
if(b == '-'){
minus = true;
b = readByte();
}
while(true){
if(b >= '0' && b <= '9'){
num = num * 10 + (b - '0');
}else{
return minus ? -num : num;
}
b = readByte();
}
}
private static long nl()
{
long num = 0;
int b;
boolean minus = false;
while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
if(b == '-'){
minus = true;
b = readByte();
}
while(true){
if(b >= '0' && b <= '9'){
num = num * 10 + (b - '0');
}else{
return minus ? -num : num;
}
b = readByte();
}
}
private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}