G2. Ruler (hard version)

昨晚的div4最后一题
上一次遇到三分好像是2021年icpc济南，那场2题就能拿银牌:(

/*
* @Author:  Hfuubigstrength
* @email:   2854614012@qq.com
* @Date:   2024-08-07 10:52:47
*/
#include <bits/stdc++.h>
// #define int long long
#define PII pair<int,int>
#define LL long long
#define fi first
#define se second
#define debug(a) cout<<#a<<"="<<a<<endl;
#define all(x) (x).begin(),(x).end()
#define pb push_back
#define sz(x) (int)x.size()
using namespace std;


void solve(){
    // int n;
    int l = 2, r = 999;
    while(l < r){
        int len = (r - l) / 3;
        int mid1 = l + len, mid2 = r - len;
        cout << "? " << mid1 << " " << mid2 << endl;
        int area; cin >> area;
        if(mid1 * mid2 == area) l = mid2 + 1;
        else if((mid1 + 1) * (mid2 + 1) == area) r = mid1;
        else if((mid2 + 1) * mid1 == area) r = mid2, l = mid1 + 1;
    }
    cout << "! " << l << endl;
}

signed main(){
    //ios::sync_with_stdio(false);cin.tie(0);
    int tt = 1;
    cin >> tt;
    while(tt -- ){
        solve();
    }
    return 0;
}

昨晚F用到的组合数预处理：

int fact[N], infact[N];

int qmi(int k, int s, int m){
    int res = 1;
    while(s){
        if(s & 1) res = (LL)res * k % mod;
        s >>= 1, k = (LL)k * k % mod;
    }
    return res;
}
int get(int a, int b){
    return (LL)fact[a] * infact[a - b] % mod * infact[b] % mod;
}

void init(){
    fact[0] = 1, infact[0] = 1;
    for(int i = 1; i <= N - 5; i ++ ){
        fact[i] = (LL)fact[i - 1] * i % mod;
        infact[i] = (LL)infact[i - 1] * qmi(i, mod - 2, mod) % mod;
    }    
}