CF1179E.Alesya and Discrete Math

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

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 $10^{18}$ .

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

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.