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F. SUM and REPLACE

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLet *D*(*x*) be the number of positive divisors of a positive integer *x*. For example, *D*(2) = 2 (2 is divisible by 1 and 2), *D*(6) = 4 (6 is divisible by 1, 2, 3 and 6).

You are given an array *a* of *n* integers. You have to process two types of queries:

- REPLACE
*l**r*— for every replace*a*_{i}with*D*(*a*_{i}); - SUM
*l**r*— calculate .

Print the answer for each SUM query.

Input

The first line contains two integers *n* and *m* (1 ≤ *n*, *m* ≤ 3·10^{5}) — the number of elements in the array and the number of queries to process, respectively.

The second line contains *n* integers *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{6}) — the elements of the array.

Then *m* lines follow, each containing 3 integers *t*_{i}, *l*_{i}, *r*_{i} denoting *i*-th query. If *t*_{i} = 1, then *i*-th query is REPLACE *l*_{i} *r*_{i}, otherwise it's SUM *l*_{i} *r*_{i} (1 ≤ *t*_{i} ≤ 2, 1 ≤ *l*_{i} ≤ *r*_{i} ≤ *n*).

There is at least one SUM query.

Output

For each SUM query print the answer to it.

Example

Input

7 6

6 4 1 10 3 2 4

2 1 7

2 4 5

1 3 5

2 4 4

1 5 7

2 1 7

Output

30

13

4

22

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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