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 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 . 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 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 . 3 27 = 7625597484987