GCD

Mr. Frog likes generating numbers! He can generate many numbers from a sequence.

For a given sequence $a_1,a_2,\cdots ,a_n$ Mr. Frog can choose two numbers l and r ($1 \leq l \leq r \leq n$) and calculate the gcd between l-th and r-th number in this sequence $g = gcd(a_l,a_{l+1},\cdots ,a_r)$. Asan expert in generating numbers, Mr. Frog wants to know how many distinct numbers can be generated by a sequence.

Mr. Frog likes challenges, so there may be many modifications in this sequence. In the i-th modification, Mr. Frog may change $a_p$ to $v_i$. After each modification, you are asked to tell how many distinct numbers can be generated by this sequence immediately!

The first line contains only one integer T, which indicates the number of test cases.

For each test case, the first line includes two numbers n, q($1 \leq n,q \leq 50000$). which indicate the length of sequence and the number of modifications.

The second line contains n numbers:$a_1,a_2,\cdots ,a_n$.

Then q lines, each line contain two numbers, $p_i,v_i(1 \leq p_i \leq n, 1 \leq v_i \leq 1000000)$.

Test data guarantee that $1 <\leq a_i \leq 1000000$ all the time and the sum of all n and q is less than or equal to $2 \times 10^5$.

For each test case, first output one line "Case #x:", where x is the case number (starting from 1). Then q lines, each line contain only one number, which is the answer to current sequence.

2
3 2
1 2 3
1 3
2 3

3 2
3 3 3
1 1
2 2

Case #1:
3
1
Case #2:
2
3

For case 1, after the first operation, 3,2,1 can be generated by the sequence 3, 2, 3. Whereas after the second operation, sequence 3, 3, 3 can generate only 3.