#9078 (Java21) No.109 N! mod M

提出ソース

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	Java21 (openjdk 21)
結果	AC
実行時間	269 ms / 5,000 ms
コード長	6,514 bytes
コンパイル時間	2,699 ms
コンパイル使用メモリ	78,792 KB
実行使用メモリ	53,480 KB
最終ジャッジ日時	2023-09-04 05:22:56
合計ジャッジ時間	4,474 ms
ジャッジサーバーID （参考情報）	judge12 / judge15

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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	AC	69 ms 50,556 KB
testcase_01	AC	269 ms 53,236 KB
testcase_02	AC	188 ms 53,324 KB
testcase_03	AC	73 ms 50,512 KB
testcase_04	AC	74 ms 50,720 KB
testcase_05	AC	185 ms 52,656 KB
testcase_06	AC	85 ms 52,440 KB
testcase_07	AC	101 ms 53,480 KB
testcase_08	AC	73 ms 50,484 KB

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ソースコード

raw source code

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)); }
}

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テストケース

ソースコード