Codeforces Round 964 (Div. 4) G2. Ruler (hard version)

G2. Ruler (hard version)

time limit per test: 1 second

memory limit per test: 256 megabytes

This is the hard version of the problem. The only difference between the two versions is that in this version, you can make at most 7 queries.

This is an interactive problem. If you are unsure how interactive problems work, then it is recommended to read the guide for participants.

We have a secret ruler that is missing one number x (2≤x≤999). When you measure an object of length y, the ruler reports the following values:

If y<x, the ruler (correctly) measures the object as having length y.

If y≥x, the ruler incorrectly measures the object as having length y+1.

The ruler above is missing the number 4, so it correctly measures the first segment as length 3 but incorrectly measures the second segment as length 6 even though it is actually 5.

You need to find the value of x. To do that, you can make queries of the following form:

? a b --- in response, we will measure the side lengths of an a×b rectangle with our ruler and multiply the results, reporting the measured area of the rectangle back to you. For example, if x=4 and you query a 3×5 rectangle, we will measure its side lengths as 3×6 and report 18 back to you.

Find the value of x. You can ask at most 7 queries.

Input

Each test contains multiple test cases. The first line of input contains a single integer t (1≤t≤1000) --- the number of test cases.

Interaction

There is no initial input for each test case. You should begin the interaction by asking a query.

To make a query, output a single line of the form ? a b (1≤a,b≤1000). In response, you will be told the measured area of the rectangle, according to our secret ruler.

When you are ready to print the answer, output a single line of the form ! x (2≤x≤999). After that, proceed to process the next test case or terminate the program if it was the last test case. Printing the answer does not count as a query.

The interactor is not adaptive, meaning that the answer is known before the participant asks the queries and doesn't depend on the queries asked by the participant.

If your program makes more than 7 queries for one set of input data, makes an invalid query, or prints the wrong value of x, then the response to the query will be −1. After receiving such a response, your program should immediately terminate to receive the verdict Wrong Answer. Otherwise, you can get an arbitrary verdict because your solution will continue to read from a closed stream.

After printing a query do not forget to output the end of line and flush the output. Otherwise, you may get Idleness limit exceeded verdict. To do this, use:

fflush(stdout) or cout.flush() in C++;

System.out.flush() in Java;

flush(output) in Pascal;

stdout.flush() in Python;

see the documentation for other languages.

Hacks

To make a hack, use the following format.

The first line should contain a single integer t (1≤t≤1000) --- the number of test cases.

The only line of each test case should contain a single integer x (2≤x≤999) --- the missing number on the ruler.

Example

Input

2

18

25

9999

Output

? 3 5

? 4 4

! 4

? 99 100

! 100

Note

In the first test, the interaction proceeds as follows.

|----------|------|---------------------------------------------------------------------------------------------------------------------------------------------------------------|
| Solution | Jury | Explanation |
| | 2 | There are 2 test cases. |
| ? 3 5 | 18 | Secretly, the jury picked x=4. The solution requests the 3×5 rectangle, and the jury responds with 3×6=18, as described in the statement. |
| ? 4 4 | 25 | The solution requests the 4×4 rectangle, which the jury measures as 5×5 and responds with 25. |
| ! 4 | | The solution has somehow determined that x=4, and outputs it. Since the output is correct, the jury continues to the next test case. |
| ? 99 100 | 1 | Secretly, the jury picked x=100. The solution requests the 99×100 rectangle, which the jury measures as 99×101 and responds with 9999. |
| ! 100 | | The solution has somehow determined that x=100, and outputs it. Since the output is correct and there are no more test cases, the jury and the solution exit. |

Note that the line breaks in the example input and output are for the sake of clarity, and do not occur in the real interaction.

【思路分析】

三分。

cpp 复制代码
#include<bits/stdc++.h>

#define i64 long long

using namespace std;

inline i64 query(i64 a, i64 b) {
    i64 tmp;
    cout << "? " << a << " " << b << endl;
    cin >> tmp;
    return tmp;
}

void solve() {
    i64 l = 2, r = 999;
    while (l < r) {
        i64 mid1 = l + (r - l) / 3, mid2 = r - (r - l) / 3;
        i64 res = query(mid1, mid2);
        if (res == mid1 * mid2) {
            l = mid2 + 1;
        } else if (res == mid1 * (mid2 + 1)) {
            l = mid1 + 1;
            r = mid2;
        } else r = mid1;
    }
    cout<<"! "<<r<<endl;
    cout.flush();
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    int t = 1;
    cin >> t;
    while (t--) {
        solve();
    }
    return 0;
}
相关推荐
YuTaoShao1 小时前
【LeetCode 热题 100】48. 旋转图像——转置+水平翻转
java·算法·leetcode·职场和发展
生态遥感监测笔记1 小时前
GEE利用已有土地利用数据选取样本点并进行分类
人工智能·算法·机器学习·分类·数据挖掘
Tony沈哲2 小时前
macOS 上为 Compose Desktop 构建跨架构图像处理 dylib:OpenCV + libraw + libheif 实践指南
opencv·算法
刘海东刘海东2 小时前
结构型智能科技的关键可行性——信息型智能向结构型智能的转变(修改提纲)
人工智能·算法·机器学习
pumpkin845143 小时前
Rust 调用 C 函数的 FFI
c语言·算法·rust
挺菜的3 小时前
【算法刷题记录(简单题)003】统计大写字母个数(java代码实现)
java·数据结构·算法
mit6.8243 小时前
7.6 优先队列| dijkstra | hash | rust
算法
2401_858286113 小时前
125.【C语言】数据结构之归并排序递归解法
c语言·开发语言·数据结构·算法·排序算法·归并排序
guygg884 小时前
基于matlab的FIR滤波器
开发语言·算法·matlab
ysh98885 小时前
PP-OCR:一款实用的超轻量级OCR系统
算法