Problem Description

Consider the set of positive integers from $1$ to $N$. Let's arrange the elements of this set in lexicographical order, for example, when $N=11$, the order should be: $1, 10, 11, 2, 3, 4, 5, 6, 7, 8, 9$.

Define the position of $K$ among the $N$ numbers as $Q(N,K)$, for example, $Q(11,2)=4$. Given integers $K$ and $M$, find the smallest $N$ such that $Q(N,K)=M$.

Input Format

The input file contains a single line with two integers $K$ and $M$.

Output Format

The output file contains a single line with the smallest $N$. If no such $N$ exists, output $0$.

Sample Input and Output

Sample Input #1

2 4

Sample Output #1

11

Sample Input #2

100000001 1000000000

Sample Output #2

100000000888888879

Notes

Data Specification

• $40\%$ of the test cases have $1 \le K, M \le 10^5$.
• $100\%$ of the test cases have $1 \le K, M \le 10^9$.

见题面 Input 部分

见题面 Output 部分