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.