結果

問題 No.665 Bernoulli Bernoulli
ユーザー uwiuwi
提出日時 2018-03-09 22:41:27
言語 Java21
(openjdk 21)
結果
AC  
実行時間 78 ms / 2,000 ms
コード長 4,816 bytes
コンパイル時間 3,722 ms
コンパイル使用メモリ 85,812 KB
実行使用メモリ 51,036 KB
最終ジャッジ日時 2024-10-10 06:47:51
合計ジャッジ時間 5,913 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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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 55 ms
50,288 KB
testcase_01 AC 53 ms
50,132 KB
testcase_02 AC 63 ms
50,440 KB
testcase_03 AC 72 ms
51,036 KB
testcase_04 AC 78 ms
50,848 KB
testcase_05 AC 64 ms
50,524 KB
testcase_06 AC 70 ms
51,008 KB
testcase_07 AC 74 ms
50,532 KB
testcase_08 AC 74 ms
50,492 KB
testcase_09 AC 70 ms
51,024 KB
testcase_10 AC 73 ms
50,576 KB
testcase_11 AC 75 ms
50,812 KB
testcase_12 AC 71 ms
50,632 KB
testcase_13 AC 66 ms
50,748 KB
testcase_14 AC 66 ms
50,980 KB
testcase_15 AC 63 ms
50,512 KB
testcase_16 AC 65 ms
50,768 KB
testcase_17 AC 63 ms
50,012 KB
testcase_18 AC 69 ms
50,984 KB
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ソースコード

diff # 

package contest180309;
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 E {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		long n = nl();
		int K = ni();
		out.println(powerSum(n, K, 1000000007, enumFIF(20000, 1000000007)));
	}
	
	public static int[][] enumFIF(int n, int mod) {
		int[] f = new int[n + 1];
		int[] invf = new int[n + 1];
		f[0] = 1;
		for (int i = 1; i <= n; i++) {
			f[i] = (int) ((long) f[i - 1] * i % mod);
		}
		long a = f[n];
		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;
		}
		invf[n] = (int) (p < 0 ? p + mod : p);
		for (int i = n - 1; i >= 0; i--) {
			invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);
		}
		return new int[][] { f, invf };
	}

	
	public static long powerSum(long n, int K, int mod, int[][] fif)
	{
		long[] ys = new long[K+2];
		for(int i = 1;i <= K+1;i++){
			ys[i] = pow(i, K, mod) + ys[i-1];
			if(ys[i] >= mod)ys[i] -= mod;
		}
		return guessDirectly2(mod, n, fif, ys);
	}
	
	public static long pow(long a, long n, long mod) {
		//		a %= mod;
		long ret = 1;
		int x = 63 - Long.numberOfLeadingZeros(n);
		for (; x >= 0; x--) {
			ret = ret * ret % mod;
			if (n << 63 - x < 0)
				ret = ret * a % mod;
		}
		return ret;
	}
	
	public static long guessDirectly2(long mod, long x, int[][] fif, long... y)
	{
		int n = y.length;
		if(0 <= x && x < n){
			return y[(int)x];
		}else{
			x %= mod;
			long s = 0;
			long big = (Long.MAX_VALUE/mod/mod-1)*mod*mod;
			long[] left = new long[n+1];
			left[0] = 1;
			for(int i = 0;i < n;i++){
				left[i+1] = left[i] * (x-i) % mod;
			}
			
			long right = 1;
			for(int i = n-1;i >= 0;i--){
				s += left[i] * right % mod * fif[1][i] % mod * fif[1][n-1-i] % mod * y[i];
				if(s >= big)s -= big;
				if(s <= -big)s += big;
				right = right * -(x-i) % mod;
			}
			s %= mod;
			if(s < 0)s += mod;
			return s;
		}
	}


	
	void run() throws Exception
	{
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
//		Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
//			@Override
//			public void run() {
//				long s = System.currentTimeMillis();
//				solve();
//				out.flush();
//				if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
//			}
//		};
//		t.start();
//		t.join();
	}
	
	public static void main(String[] args) throws Exception { new E().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private 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 boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private 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 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 int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private long[] nal(int n)
	{
		long[] a = new long[n];
		for(int i = 0;i < n;i++)a[i] = nl();
		return a;
	}
	
	private 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 int[][] nmi(int n, int m) {
		int[][] map = new int[n][];
		for(int i = 0;i < n;i++)map[i] = na(m);
		return map;
	}
	
	private int ni() { return (int)nl(); }
	
	private 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) { System.out.println(Arrays.deepToString(o)); }
}
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