一本通1654：车的放置

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cctype>
#include <algorithm>
using namespace std;
const int maxn = 1005, TT = 100003;
typedef long long LL;
int a, b, c, d, k, fac[maxn * 2], inv[maxn * 2], ans;
inline int QP(int a, int b) {
    int ret = 1, w = a;

    while (b) {
        if (b & 1)
            ret = (LL)ret * w % TT;

        w  = (LL)w * w % TT;
        b >>= 1;
    }

    return ret;
}
inline int C(int n, int m) {
    return (LL)fac[n] * inv[m] % TT * inv[n - m] % TT;
}
inline int P(int n, int m) {
    return (LL)fac[n] * inv[n - m] % TT;
}
int main() {
    scanf("%d%d%d%d%d", &a, &b, &c, &d, &k);
    fac[0] = 1;

    for (int i = 1; i <= 2000; i++)
        fac[i] = fac[i - 1] * i % TT;

    inv[2000] = QP(fac[2000], TT - 2);

    for (int i = 1999; i >= 0; i--)
        inv[i] = inv[i + 1] * (i + 1) % TT;

    for (int i = 0; i <= k; i++) {
        if (i > b || i > a || k - i < 0 || a + c - i < 0 || k - i > a + c - i || k - i > d)
            continue;

        ans = (ans + (LL)C(b, i) * P(a, i) % TT * C(d, k - i) % TT * P(a + c - i, k - i)) % TT;
    }

    printf("%d\n", ans);
    return 0;
}