Recursively find sum of digits
Submissions: 675   Accuracy:

11.44%

  Difficulty: Easy   Marks: 2

We define a recursive function f(n) which takes a positive integer n as input and does the following:

 

f(n):

if n < 10

    return n

else return f( sum_of_digits(n) )

 

where sum_of_digits(n) returns the sum of the digits of the positive integer n.

Given two positive integers A and B,  the task is to find the value of f(AB).

 

Input:
The first line of input contains a single integer T denoting the number of test cases. Then T test cases follow. Each test case consists of exactly one line. This line consists of two space separated positive integers A and B.


Output:

Corresponding to each test case, in a new line, print the value of f(AB).


Constraints:

1 ≤ T ≤ 200

1 ≤ A, B ≤ 109       


Example:

Input

3
6 6
7 3
1000 1

Output

9
1
1

Explanation:

f(66) = f(46656) = f(27) = f(9) = 9

f(73) = f(343) = f(10) = f(1) = 1

f(1000) = f(1) = 1

** For More Input/Output Examples Use 'Expected Output' option **

Author: Hemang Sarkar


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