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You were late in the maths class which is taught by Geek. Now to punish you, Geek gave you a problem to solve. Given four integer numbers **A**, **B**, **C**, and **N**, Geek wants you to find **f(f(..........f(a)))** **N** times. Where f(x) = ((x/b) * c) - 1.

Output can be represented as a fraction **P/Q**, you have to output **P*Q ^{-1}** modulo 10

**Input: **

1. The first line of the input contains a single integer* * **T** denoting the number of test cases. The description of **T** test cases follows.

2. The first line of each test case contains four space-separated integers **A, B, C, **and** N**.

**Output:** For each test case, print** **the answer.

**Constraints:**

1. 1 ≤ T ≤ 10

2. 1 ≤ A, B, C ≤ 10^{9}

3. 1 ≤ N ≤ 10^{3}

**Example:**

Input:2 1 3 4 1 1 3 4 2Output:333333336 444444447

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Division II

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