CF1493D.GCD of an Array

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 $q$ ( $1 \le n, q \le 2 \cdot 10^5$ ).

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le 2 \cdot 10^5$ ) — 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 $x$ ( $1 \le i \le n$ , $1 \le x \le 2 \cdot 10^5$ ).

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.