Bob is writing a program that solves the following problem:
You are given the numbers \(a,b\) to display the infinite sequence of numbers \(a, a + b, a + 2*b, ..., a + N*b, a.. (N+1)*b,... \). Bob has made a mistake, he namely forgot to draw a space for the division between the numbers, resulting in a long line of numbers. In order not to correct the mistake, Bob decided to find out how to find the \(k^{th}\) digit in the formed line (numbering of digits begins with one).
Bob could not find a good solution, so he asks you for help.
Input format
- The first line contains a number \(T\) denoting the number of tests.
- The first line of each test contains four integers \(a, b, k\).
Output format
Print the \(k^{th}\) digit for each test.
Constraints
\(1 ≤ T ≤ 10 \)
\(1 ≤ a, b ≤ 10^3\)
\( 1 ≤ k ≤ 10^9\)
2 3 5 9 2 7 10
2 7
In the first case, the infinite sequence of numbers for \(a = 3, b = 5\) is --> \((3,8,13,18,23,28,...)\). The long line is \(3813182328...\).
\(K^{th}\) digit is 2
In the second case, the infinite sequence of numbers for \(a = 2, b = 7\) is --> \((2,9,16,23,30,37,...)\). The long line is \(2916233037...\).
\(K^{th}\) digit is 7
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