I know the k-th integer

Time Limit: 1000MS

Memory Limit: 65536K

Description

Sort the first n integers 1,2,3,...,n-1,n in lexicographical order, and the k-th integer is known as m. Can you tell me the smallest n? For example,when n=11, the order is 1, 10, 11, 2, 3, 4, 5, 6, 7, 8, 9. And the 4-th integer is 2.

Input

The input contains many test cases ended with EOF. Each test case contains only one line of two integers, k and m. 1 ≤ k, m ≤ 10^9

Output

For each test case output the smallest n in a single line. If there is no such n, just output 0.

Sample Input

4 2
2 1
1000 25

Sample Output

11
0
1831

Hint

Source

POJ Monthly Contest – 2009.04.05, windy792677

提交代码