Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Power Tower

time limit per test

4.5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPriests of the Quetzalcoatl cult want to build a tower to represent a power of their god. Tower is usually made of power-charged rocks. It is built with the help of rare magic by levitating the current top of tower and adding rocks at its bottom. If top, which is built from *k* - 1 rocks, possesses power *p* and we want to add the rock charged with power *w*_{k} then value of power of a new tower will be {*w*_{k}}^{p}.

Rocks are added from the last to the first. That is for sequence *w*_{1}, ..., *w*_{m} value of power will be

After tower is built, its power may be extremely large. But still priests want to get some information about it, namely they want to know a number called cumulative power which is the true value of power taken modulo *m*. Priests have *n* rocks numbered from 1 to *n*. They ask you to calculate which value of cumulative power will the tower possess if they will build it from rocks numbered *l*, *l* + 1, ..., *r*.

Input

First line of input contains two integers *n* (1 ≤ *n* ≤ 10^{5}) and *m* (1 ≤ *m* ≤ 10^{9}).

Second line of input contains *n* integers *w*_{k} (1 ≤ *w*_{k} ≤ 10^{9}) which is the power of rocks that priests have.

Third line of input contains single integer *q* (1 ≤ *q* ≤ 10^{5}) which is amount of queries from priests to you.

*k*^{th} of next *q* lines contains two integers *l*_{k} and *r*_{k} (1 ≤ *l*_{k} ≤ *r*_{k} ≤ *n*).

Output

Output *q* integers. *k*-th of them must be the amount of cumulative power the tower will have if is built from rocks *l*_{k}, *l*_{k} + 1, ..., *r*_{k}.

Example

Input

6 1000000000

1 2 2 3 3 3

8

1 1

1 6

2 2

2 3

2 4

4 4

4 5

4 6

Output

1

1

2

4

256

3

27

597484987

Note

3^{27} = 7625597484987

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/21/2018 12:11:53 (f1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|