One day, Eevee received an equation from her best friend:
ax x by = cz,
where c and z are given integers.
She wants to count the number of integral solutions (a,x,b,y) of this equation which satisfies 1≤ a,b ≤ m, 0 ≤ x,y ≤ m.
输入描述:
The input starts with one line containing exactly one integer T which is the number of test cases. (1 ≤ T≤ 1000)
Each test case contains one line with three integers c, z and m. (1 ≤ c, m ≤ 105,0 ≤ z ≤ 105)
输出描述:
For each test case, output "Case #x: y" in one line (without quotes), where x is the test case number (starting from 1) and y is the number of integral solutions.