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문제

Lately, Slavko’s been studying sequences of natural numbers. He finds a sequence interesting if the greatest common divisor of all the elements from the sequence is greater than 1.

Yesterday, he found a sequence consisting of N natural numbers in his garage. Since he was really bored, he decided to keep himself occupied by asking simple queries. Each query can be one of the two types:

  1. Change the value at position X in the sequence to V.
  2. Determine the number of interesting contiguous subarrays contained in the interval [L, R] of the sequence.

입력

The first line of input contains the numbers N and Q (1 ≤ N, Q ≤ 105), representing the number of elements in the sequence and the number of queries, respectively.

The following line contains N natural numbers Ai (1 ≤ Ai ≤ 109) that represent the numbers in the initial sequence.

Each of the following Q lines contains a query of the following form:

  • The first number in the line can be 1 or 2 and represents the type of the query.
  • If the query is of type 1, two numbers follow, X (1 ≤ X ≤ N) and V (1 ≤ V ≤ 109) from the task.
  • If the query is of type 2, two numbers follow, L and R (1 ≤ L ≤ R ≤ N) that represent the left and right interval boundary.

출력

For each query of type 2, output the number of interesting contiguous subarrays from the task.

예제 입력 1

5 1
8 4 3 9 1
2 2 5

예제 출력 1

4

예제 입력 2

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

예제 출력 2

6
1

예제 입력 3

4 3
2 2 2 2
2 1 4
1 2 3
2 1 4

예제 출력 3

10
5

힌트

Clarification​ ​of​ ​the​ ​first​ ​test​ ​case: The interval from the 2 nd to the 5 th position consists of numbers (4, 3, 9, 1). In it, the following are interesting contiguous subarrays (denoted with square brackets): [4]​ 3 9 1, 4 [3]​ ​9 1, 4 3 [9]​ 1, 4 [3​ ​9]​ 1