Bob loves squares! More specifically, he loves perfect squares. He has a collection of ~N~ cards, numbered from ~0~ to ~N-1~, each with a value written on it.

Bob has ~Q~ queries of the form l r. He would like to know if the product of the values on the cards ~l~ to ~r~, inclusive would form a perfect square.

Input Specification

The first line contains two integers, ~N~ and ~Q~, such that ~N, Q~ ~(1 \le N, Q \le 10^5)~

The second line contains ~N~ integers, the values on the cards, ~a_i~ ~(1 \le a_i \le 10^5)~

The next ~Q~ lines, contain queries of the form l r such that ~l, r~ ~(0 \le l \le r < N)~

Output Specification

For each query, print on a separate line yes if the product is a perfect square and no if it is not.

Subtasks

Subtask 1 (30%)

~N, Q, a_i \le 1000~

Subtask 2 (70%)

No further constraints.

Sample Input

4 3
9 3 5 15
0 0
1 2
1 3

Sample Output

yes
no
yes

Sample Explanation 1

From ~0~ to ~0~, the only number is ~9~, which is a perfect square.

From ~1~ to ~2~, the product is ~15~, which is not a perfect square.

From ~1~ to ~3~, the product is ~225~, which is a perfect square.