Yaroslav has an array p = p₁, p₂, ..., p_n (1 ≤ p_i ≤ n), consisting of n distinct integers. Also, he has m queries:

Query number i is represented as a pair of integers l_i, r_i (1 ≤ l_i ≤ r_i ≤ n).
The answer to the query l_i, r_i is the number of pairs of integers q, w (l_i ≤ q, w ≤ r_i) such that p_q is the divisor of p_w.

Help Yaroslav, answer all his queries.

Input

The first line contains the integers n and m (1 ≤ n, m ≤ 2·10⁵). The second line contains n distinct integers p₁, p₂, ..., p_n (1 ≤ p_i ≤ n). The following m lines contain Yaroslav's queries. The i-th line contains integers l_i, r_i (1 ≤ l_i ≤ r_i ≤ n).

Output

Print m integers — the answers to Yaroslav's queries in the order they appear in the input.

Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

Yaroslav and Divisors

Examples