Tokitsukaze has a permutation $p$ of length $n$.

Let's call a segment $[l,r]$ beautiful if there exist $i$ and $j$ satisfying $p_i \cdot p_j = \max\{p_l, p_{l+1}, \ldots, p_r \}$, where $l \leq i < j \leq r$.

Now Tokitsukaze has $q$ queries, in the $i$-th query she wants to know how many beautiful subsegments $[x,y]$ there are in the segment $[l_i,r_i]$ (i. e. $l_i \leq x \leq y \leq r_i$).

Input

The first line contains two integers $n$ and $q$ ($1\leq n \leq 2 \cdot 10^5$; $1 \leq q \leq 10^6$) — the length of permutation $p$ and the number of queries.

The second line contains $n$ distinct integers $p_1, p_2, \ldots, p_n$ ($1 \leq p_i \leq n$) — the permutation $p$.

Each of the next $q$ lines contains two integers $l_i$ and $r_i$ ($1 \leq l_i \leq r_i \leq n$) — the segment $[l_i,r_i]$ of this query.

Output

For each query, print one integer — the numbers of beautiful subsegments in the segment $[l_i,r_i]$.

见题面 Input 部分

见题面 Output 部分

In the first example, for the first query, there are $2$ beautiful subsegments — $[1,2]$ and $[1,3]$.