Teacher Mai finds that many problems about arithmetic function can be reduced to the following problem:
Maintain an array a with index from 1 to l. There are two kinds of operations:
1. Add v to a
x for every x that gcd(x,n)=d.
2. Query
There are multiple test cases, terminated by a line "0 0".
For each test case, the first line contains two integers l,Q(1<=l,Q<=5*10^4), indicating the length of the array and the number of the operations.
In following Q lines, each line indicates an operation, and the format is "1 n d v" or "2 x" (1<=n,d,v<=2*10^5,1<=x<=l).
For each case, output "Case #k:" first, where k is the case number counting from 1.
Then output the answer to each query.