You are given a cluster an of length n. You are approached to deal with q inquiries of the accompanying organization: given integers I and x, duplicate computer based intelligence by x. In the wake of handling each inquiry you really wanted to output the best normal divisor (GCD) of all components of the cluster a.
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You are given a cluster an of length n. You are approached to deal with q inquiries of the accompanying organization: given integers I and x, duplicate computer based intelligence by x.
In the wake of handling each inquiry you really wanted to output the best normal divisor (GCD) of all components of the cluster a.
Since the appropriate response can be excessively huge, you are approached to output it modulo 109+7.
Input
The principal line contains two integers — n and q (1≤n,q≤2⋅105).
The subsequent line contains n integers a1,a2,… ,an (1≤
The following q lines contain inquiries in the accompanying arrangement: each line contains two integers I and x (1≤i≤n, 1≤x≤2⋅105).
Output
Print q lines: in the wake of handling each inquiry output the GCD of all components modulo 109+7 on a different line.
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