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E. Alesya and Discrete Math

time limit per test

5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputWe 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

Input

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 $$$10^{18}$$$.

Output

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 $$$f_i(l_j) < f_i(l_j + 1)$$$.

Example

Input

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

Output

0 1 1 2 2 3 3 4 4 4 5

Note

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.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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