26. Intelligence Agency Digit Sum

Difficulty: easy · Math

Problem

An intelligence agency is studying coded reports, each made of two numbers `N` and `R`. To decode a report: 1. Add up all the digits of `N`. 2. Repeat that sum `R` times, i.e. compute `R * (digit sum of N)`. 3. Keep adding the digits of the result until a single digit remains. Print that single digit. If `R` is `0`, print `0`. For example, `N = 99`, `R = 3`: the digit sum is 18, `3 * 18 = 54`, and `5 + 4 = 9`.

Input

- Line 1: the integer `N`. - Line 2: the integer `R`.

Output

Print the resulting single digit.

Example 1

Input:
99
3
Output:
9

Explanation: Digit sum 9+9 = 18; 18*3 = 54; 5+4 = 9.

Example 2

Input:
1234
2
Output:
2

Explanation: Digit sum 10; 10*2 = 20; 2+0 = 2.

Example 3

Input:
57
0
Output:
0

Explanation: R is 0, so the output is 0.

Constraints

- 1 <= N <= 10^18 - 0 <= R <= 10^9

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