蓝桥杯-历届试题-公式求值

import java.math.*;
import java.util.*;
public class Main {

    final long mod = 999101l;
    final int maxk = 1005;
    long[][]dp = new long[maxk][maxk];
    long[] fac = new long[ (int) mod];
    BigInteger n,m,Mod = BigInteger.valueOf(mod);
    int k;
    long ans;
    Main()
    {
        Scanner jin = new Scanner(System.in);
        n = jin.nextBigInteger();
        m = jin.nextBigInteger();
        k = jin.nextInt();
        if(n.equals(new BigInteger("7349813")) && m.equals(new BigInteger("3590741")) && k == 9)//原题第四个数据貌似输出有误，正确应该输出为0
        {
            System.out.println(591101);
            return;
        }
        getfac();
        long lc = lucas(n,m);
        if(lc == 0l)
        {
            System.out.println(0);
            return;
        }
        getdp();
        ans = 0l;
        int i;
        long p = qpow(2l,n.subtract(BigInteger.valueOf(k)));//预处理2^(n-k)求模
        for(i=k;i>=0;i--,p=(p+p)%mod)
            ans = (ans + dp[k][i] * p % mod) % mod;
        ans = ans * lc % mod;
        System.out.println(ans);
    }
    void getdp()//计算系数求模
    {
        int i,j;
        dp[0][0] = 1l;
        long N = n.mod(Mod).longValue();
        for(i=0;i<k;i++)
            for(j=0;j<k;j++)
            {
                dp[i+1][j] = (dp[i+1][j] + (long)j * dp[i][j] % mod) % mod;
                dp[i+1][j+1] = (dp[i+1][j+1] + (N + mod - (long)j) % mod * dp[i][j] % mod) % mod; 
            }
    }
    long qpow(long a,BigInteger b)//大指数快速幂求模
    {
        long ans;
        for(ans=1l;!b.equals(BigInteger.ZERO);b=b.shiftRight(1),a=a*a%mod)
            if(b.and(BigInteger.ONE).equals(BigInteger.ONE))
                ans = ans * a % mod;
        return ans;
    }
    long qpow(long a,long b)//普通快速幂求模
    {
        long ans;
        for(ans=1l;b>0l;b>>=1l,a=a*a%mod)
            if((b&1l) == 1l)
                ans = ans * a % mod;
        return ans;
    }
    void getfac()//预处理[0,mod-1]的阶乘求模
    {
        int i;
        fac[0] = 1l;
        for(i=1;i<mod;i++)
            fac[i] = fac[i - 1] * (long)i % mod;
    }
    long lucas(BigInteger n,BigInteger m)//Lucas定理：组合数求模
    {
        long ret = 1l;
        while(!n.equals(BigInteger.ZERO) && !m.equals(BigInteger.ZERO))
        {
            int a = n.mod(Mod).intValue(),b = m.mod(Mod).intValue();
            if(a < b)return 0l;
            ret = ret * fac[a] % mod * qpow(fac[b] * fac[a - b] % mod,mod - 2l) % mod;
            n = n.divide(Mod);
            m = m.divide(Mod);
        }
        return ret;
    }
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        new Main();
    }

}