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D. Yaroslav and Divisors

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYaroslav has an array *p* = *p*_{1}, *p*_{2}, ..., *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* ≤ 2·10^{5}). The second line contains *n* distinct integers *p*_{1}, *p*_{2}, ..., *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.

Examples

Input

1 1

1

1 1

Output

1

Input

10 9

1 2 3 4 5 6 7 8 9 10

1 10

2 9

3 8

4 7

5 6

2 2

9 10

5 10

4 10

Output

27

14

8

4

2

1

2

7

9

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