## Description:

There is a mysterious organization called GCD. They get a permutation P, permutation is a sequence of length N, only consists of number 1 to N and each number appears only once.

They want to gain magic power from this permutation. For the interval [L, R] they can get power:

$$$\sum\limits_{i=L}^R\sum\limits_{j=i+1}^R\sum\limits_{k=j+1}^R (gcd(P[i], P[j]) == P[k]) \cdot P[k]$$$

Now they have M queries, for each query can you help them calculate how many power they can get？

## Input:

The first line is an integer T which indicates the case number.

And as for each case, first line is two integer N and M which indicates the length of permutation and number of query.

Next line is N integer which indicate the permutation P

Next M line, for each line is two integer L and R which indicate each query.

Limit

$$$1 \leq T \leq 100$$$

$$$1 \leq N, M \leq100000$$$

$$$1 \leq Pi \leq N$$$, for any pair $$$(i, j)$$$, $$$Pi \neq Pj$$$

$$$1 \leq Li \leq Ri \leq N$$$

About 95% test case: $$$1 \leq N \leq 1000$$$

Other test case: $$$1 \leq N \leq 100000$$$

## Output:

As for each case, you need to output M integer which indicate the answer of each query.

## Sample Input:

2
3 1
3 2 1
1 3
6 3
6 5 4 3 2 1
1 6
2 6
3 5

## Sample Output:

1
8
5
0