Task from an old DPA

Rows (strings of digits) are constructed according to the following rule:

The first row consists of a single character, the digit "1". Each subsequent row is formed by first writing the row number (without leading zeros), followed by appending the previous row twice.

Here are the first 4 rows created according to this rule:

1. 1

2. 211

3. 3211211

4. 432112113211211

For instance, the 11-th row will begin as follows:

11. 1110987...

Given N and K, determine which digit appears in the N-th row at the K-th position, or if the row's length is less than K.

Input

Two natural numbers N and K are provided (1 ≤ N ≤ 100000, 1 ≤ K ≤ 10^15).

Output

Identify and output the digit located at the K-th position in the N-th row. If the N-th row is shorter than K, output -1 (minus one).

Examples