## BIGSEQ - Sequence

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You are given the sequence of all K-digit binary numbers: 0, 1,..., 2K-1. You need to fully partition the sequence into M chunks. Each chunk must be a consecutive subsequence of the original sequence. Let Si (1 ≤ i ≤ M) be the total number of 1's in all numbers in the ith chunk when written in binary, and let S be the maximum of all Si, i.e. the maximum number of 1's in any chunk. Your goal is to minimize S.

### Input

In the first line of input, two numbers, K and M (1 ≤ K ≤ 100, 1 ≤ M ≤ 100, M ≤ 2^K), are given, separated by a single space character.

### Output

In one line of the output, write the minimum S that can be obtained by some split. Write it without leading zeros. The result is not guaranteed to fit in a 64-bit integer.

### Example

```Input:
3 4

Output:
4
```

 Added by: Minilek Date: 2008-01-10 Time limit: 4.924s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ERL JS-RHINO NODEJS PERL6 VB.NET Resource: MIT 1st Team Contest 2007