Priests 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 w₁, ..., w_m value of power will be

$\text{[math]}$

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 ≤ 10⁵) and m (1 ≤ m ≤ 10⁹).

Second line of input contains n integers w_k (1 ≤ w_k ≤ 10⁹) which is the power of rocks that priests have.

Third line of input contains single integer q (1 ≤ q ≤ 10⁵) 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.

Note

3²⁷ = 7625597484987

Power Tower

Examples