Codeforces 711E ZS and The Birthday Paradox 数学

ZS and The Birthday Paradox

感觉里面有好多技巧。。

#include<bits/stdc++.h>
#define LL long long
#define fi first
#define se second
#define mk make_pair
#define PLL pair<LL, LL>
#define PLI pair<LL, int>
#define PII pair<int, int>
#define SZ(x) ((int)x.size())
#define ull unsigned long long
using namespace std;

const int N = 1e6 + 7;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e6 + 3;
const double eps = 1e-8;

LL n, k;

LL power(LL a, LL b) {
    b %= mod - 1;
    LL ans = 1;
    while(b) {
        if(b & 1) ans = ans * a % mod;
        a = a * a % mod; b >>= 1;
    }
    return ans;
}

int main() {
    scanf("%lld%lld", &n, &k);
    if(n < 63 && (1ll << n) < k) {
        puts("1 1");
    } else {
        LL num = 0;
        for(LL i = k - 1; i; i /= 2) num += i / 2;
        LL A = power(2, n), B = 1;
        for(LL i = 1; i < k; i++) {
            B = B * (A - i) % mod;
            if(A == i) break;
        }
        LL inv = power(power(2, num), mod - 2);
        B = B * inv % mod;
        A = power(A, k - 1) * inv % mod;
        printf("%lld %lld\n", (A - B + mod) % mod, A);
    }
    return 0;
}

/*
*/