题目

代码

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int mod = 1e9 + 7;
const int N = 1e5 + 10;
int r[N], c[N], f[2 * N];
int nr[N], nc[N], nn, nm;
int cntr[N], cntc[N];
int n, m, t;

void init(int n) {
    f[0] = f[1] = 1;
    for (int i = 2; i <= n; i++)
        f[i] = (ll)f[i - 1] * i % mod;
}

ll qmi(ll base, int expo) {
    ll retv = 1;
    while (expo) {
        if (expo & 1)
            retv = retv * base % mod;
        base = base * base % mod;
        expo >>= 1;
    }
    return retv;
}

void discretize() {
    int last = -1;
    for(int i = 1; i <= n; i++) {
        if(nr[i] > last) ++nn, cntr[nn]++, last = nr[i];
        else cntr[nn]++;
    }
    
    last = -1;
    for(int i = 1; i <= m; i++) {
        if(nc[i] > last) ++nm, cntc[nm]++, last = nc[i];
        else cntc[nm]++;
    }
    
    cntr[0] = 1;
    for(int i = 1; i <= nn; i++)
        cntr[i] = (ll)cntr[i] * cntr[i-1] % mod;
    
    cntc[0] = 1;
    for(int i = 1; i <= nm; i++)
        cntc[i] = (ll)cntc[i] * cntc[i-1] % mod;
    
    nn = unique(nr+1, nr+n+1) - nr - 1;
    nm = unique(nc+1, nc+m+1) - nc - 1;
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    
    init(2e5);

    cin >> n >> m >> t;
    for (int i = 1; i <= n; i++)
        cin >> r[i], nr[i] = r[i];
    for (int i = 1; i <= m; i++)
        cin >> c[i], nc[i] = c[i];

    sort(nr + 1, nr + n + 1);
    sort(nc + 1, nc + m + 1);

    discretize();

    while (t--) {
        int sr, sc, tr, tc;
        cin >> sr >> sc >> tr >> tc;
        if ((r[tr] <= r[sr] && tr != sr) || (c[tc] <= c[sc] && tc != sc)) {
            cout << 0 << '\n';
            continue;
        }

        int srp = lower_bound(nr + 1, nr + nn + 1, r[sr]) - nr;
        int trp = lower_bound(nr + 1, nr + nn + 1, r[tr]) - nr;
        int scp = lower_bound(nc + 1, nc + nm + 1, c[sc]) - nc;
        int tcp = lower_bound(nc + 1, nc + nm + 1, c[tc]) - nc;
        int drp = trp - srp;
        int dcp = tcp - scp;
        int ans = (ll)f[drp + dcp] * qmi(f[drp], mod - 2) % mod * qmi(f[dcp], mod - 2) % mod;
        if(drp) ans = (ll)ans * cntr[trp-1] % mod * qmi(cntr[srp], mod-2) % mod;
        if(dcp) ans = (ll)ans * cntc[tcp-1] % mod * qmi(cntc[scp], mod-2) % mod;
        cout << ans << '\n';
    }
}