Alesya and Discrete Math

题意翻译

## 题目描述 **这是一道交互题** 有 $n$ 个函数 $f_1,f_2,\cdots,f_n$，定义域为 $0\sim 10^{18}$ 以内的整数，满足 $\forall x,f(x)=f(x-1)+1$ 或者 $f(x)=f(x-1)$ ，并且 $f(0)=0,f(10^{18})=L$ 。保证 $n$ 是 $L$ 的因数。 你可以询问一个函数在任意一个点的值，构造一组答案 $(l_1,r_1),(l_2,r_2),\cdots,(l_n,r_n)$ ，使得 $\forall i\in[1,n],f_i(r_i)-f_i(l_i)\ge \frac{L}{n}$ ，且线段 $[l_i,r_i]$ 互不相交（只有端点重合不算相交）。你最多可以询问 $2\cdot 10^5$ 次。 ## 输入格式 一行两个整数$n,L(1\le n\le 1000,1\le L\le 10^{18})$，$n$ 是 $L$ 的因数 ## 交互格式 询问一个函数在任意一个点的值：输出`?`（ASCII码63），跟着两个整数 $i$ 和 $x$ （ $1\le i\le n,0\le x\le 10^{18}$ ），表示询问 $f_i(x)$ 的值。然后清空缓冲区。 你不能询问超过 $2\cdot 10^5$ 次。 你可以使用如下语句来清空缓冲区： - 对于 C/C++：`fflush(stdout)`； - 对于 Java：`System.out.flush()`； - 对于 Python：`stdout.flush()`； - 对于 Pascal：`flush(output)`； - 对于其他语言，请自行查阅对应语言的帮助文档。 然后你需要从标准输入中读入一个整数，代表评测机返回的结果。 输出答案：输出一行`！`（ASCII码33）。接着输出 $n$ 行，第 $i$ 行两个整数 $l_i,r_i$ ，用空格分开。

题目描述

We call a function good if its domain of definition is some set of integers and if in case it's defined in $ x $ and $ x-1 $ , $ f(x) = f(x-1) + 1 $ or $ f(x) = f(x-1) $ . Tanya has found $ n $ good functions $ f_{1}, \ldots, f_{n} $ , which are defined on all integers from $ 0 $ to $ 10^{18} $ and $ f_i(0) = 0 $ and $ f_i(10^{18}) = L $ for all $ i $ from $ 1 $ to $ n $ . It's an notorious coincidence that $ n $ is a divisor of $ L $ . She suggests Alesya a game. Using one question Alesya can ask Tanya a value of any single function in any single point. To win Alesya must choose integers $ l_{i} $ and $ r_{i} $ ( $ 0 \leq l_{i} \leq r_{i} \leq 10^{18} $ ), such that $ f_{i}(r_{i}) - f_{i}(l_{i}) \geq \frac{L}{n} $ (here $ f_i(x) $ means the value of $ i $ -th function at point $ x $ ) for all $ i $ such that $ 1 \leq i \leq n $ so that for any pair of two functions their segments $ [l_i, r_i] $ don't intersect (but may have one common point). Unfortunately, Tanya doesn't allow to make more than $ 2 \cdot 10^{5} $ questions. Help Alesya to win! It can be proved that it's always possible to choose $ [l_i, r_i] $ which satisfy the conditions described above. It's guaranteed, that Tanya doesn't change functions during the game, i.e. interactor is not adaptive

输入输出格式

输入格式

The first line contains two integers $ n $ and $ L $ ( $ 1 \leq n \leq 1000 $ , $ 1 \leq L \leq 10^{18} $ , $ n $ is a divisor of $ L $ ) — number of functions and their value in $ 10^{18} $ .

输出格式

When you've found needed $ l_i, r_i $ , print $ "!" $ without quotes on a separate line and then $ n $ lines, $ i $ -th from them should contain two integers $ l_i $ , $ r_i $ divided by space. Interaction To ask $ f_i(x) $ , print symbol "?" without quotes and then two integers $ i $ and $ x $ ( $ 1 \leq i \leq n $ , $ 0 \leq x \leq 10^{18} $ ). Note, you must flush your output to get a response. After that, you should read an integer which is a value of $ i $ -th function in point $ x $ . You're allowed not more than $ 2 \cdot 10^5 $ questions. To flush you can use (just after printing an integer and end-of-line): - fflush(stdout) in C++; - System.out.flush() in Java; - stdout.flush() in Python; - flush(output) in Pascal; - See the documentation for other languages. Hacks: Only tests where $ 1 \leq L \leq 2000 $ are allowed for hacks, for a hack set a test using following format: The first line should contain two integers $ n $ and $ L $ ( $ 1 \leq n \leq 1000 $ , $ 1 \leq L \leq 2000 $ , $ n $ is a divisor of $ L $ ) — number of functions and their value in $ 10^{18} $ . Each of $ n $ following lines should contain $ L $ numbers $ l_1 $ , $ l_2 $ , ... , $ l_L $ ( $ 0 \leq l_j < 10^{18} $ for all $ 1 \leq j \leq L $ and $ l_j < l_{j+1} $ for all $ 1 < j \leq L $ ), in $ i $ -th of them $ l_j $ means that $ f_i(l_j) < f_i(l_j + 1) $ .

输入输出样例

输入样例 #1

5 5
? 1 0
? 1 1
? 2 1
? 2 2
? 3 2
? 3 3
? 4 3
? 4 4
? 5 4
? 5 5
!
0 1
1 2
2 3
3 4
4 5

输出样例 #1

0
1
1
2
2
3
3
4
4
4
5

说明

In the example Tanya has $ 5 $ same functions where $ f(0) = 0 $ , $ f(1) = 1 $ , $ f(2) = 2 $ , $ f(3) = 3 $ , $ f(4) = 4 $ and all remaining points have value $ 5 $ . Alesya must choose two integers for all functions so that difference of values of a function in its points is not less than $ \frac{L}{n} $ (what is $ 1 $ here) and length of intersection of segments is zero. One possible way is to choose pairs $ [0 $ , $ 1] $ , $ [1 $ , $ 2] $ , $ [2 $ , $ 3] $ , $ [3 $ , $ 4] $ and $ [4 $ , $ 5] $ for functions $ 1 $ , $ 2 $ , $ 3 $ , $ 4 $ and $ 5 $ respectively.