B'You are given an array a of length n . You are asked to process q queries of the following format: given integers i and x , multiply a_i by x . After processing each query you need to output the greatest common divisor (GCD) of all elements of the array a . Since the answer can be too large, you are asked to output it modulo 10^9+7 . The first line contains two integers -- n and q ( 1 <= n, q <= 2 cdot 10^5 ). The second line contains n integers a_1, a_2, ldots, a_n ( 1 <= a_i <= 2 cdot 10^5 ) -- the elements of the array a before the changes. The next q lines contain queries in the following format: each line contains two integers i and x ( 1 <= i <= n , 1 <= x <= 2 cdot 10^5 ). Print q lines: after processing each query output the GCD of all elements modulo 10^9+7 on a separate line. After the first query the array is [12, 6, 8, 12] , operatorname{gcd}(12, 6, 8, 12) = 2 . After the second query -- [12, 18, 8, 12] , operatorname{gcd}(12, 18, 8, 12) = 2 . After the third query -- [12, 18, 24, 12] , operatorname{gcd}(12, 18, 24, 12) = 6 . Here the operatorname{gcd} function denotes the greatest common divisor. '...