## BIGSEQ - Sequence

You are given the sequence of all K-digit binary numbers:
0, 1,..., 2^{K}-1.
You need to fully partition the sequence into M chunks. Each chunk
must be a consecutive subsequence of
the original sequence. Let S_{i} (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 S_{i},
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 4Output: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 |