POJ 1091 跳蚤（分解质因数 ＋ 容斥 ＋ 大数）

import java.util.*;
import java.math.*;

public class Main{
    public static int fac[] = new int[105];
    public static int re[] = new int[105];
    public static int cnt = 0, n, m;
    public static BigInteger fnum;

    public static void Divide(int x){       //分解质因数
        for(int i = 2; i <= (int)Math.sqrt(x); i++){
            if(x % i == 0){
                fac[cnt ++] = i;
                while(x % i == 0){
                    x = x / i;
                }
            }
        }
        if(x > 1)
            fac[cnt ++] = x;
    }

    public static void DFS(int pos, int cur, int num){
        if(cur == num){
            BigInteger t = BigInteger.valueOf(m);
            for(int i = 0; i < cur; i++)
                //t表示gcd值为num个素数相乘得到时(设乘积为mul)每个元素可能的值即(m / mul)
                //比如m＝18，mul＝6时，每个元素可能的值有3个：6 12 18 
                t = t.divide(BigInteger.valueOf(re[i]));
            //每个位置有t种选择，共有n各位置，所以当前集合元素个数为t^n 
            fnum = fnum.add(t.pow(n));
            return;
        }
        for(int i = pos; i < cnt; i++){
            re[cur] = fac[i];
            DFS(i + 1, cur + 1, num);
        }
    }

    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        while(in.hasNext())
        {
            n = in.nextInt();
            m = in.nextInt();
            Divide(m);
            BigInteger extra = BigInteger.ZERO;
            for(int i = 1; i <= cnt; i++){
                fnum = BigInteger.ZERO; //fnum存的是gcd集合元素个数
                DFS(0, 0, i);
                if(i % 2 == 1)  //容斥
                    extra = extra.add(fnum);
                else
                    extra = extra.subtract(fnum);
            }
            System.out.println(BigInteger.valueOf(m).pow(n).subtract(extra));

        }
    }   
}