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#F2047. Sereja and Sets

    ID: 2053 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 9 上传者: 标签>动态规划挑战难度共享题库Codeforces英文题面题目来源题面语言

Sereja and Sets

题目描述

E. Sereja and Sets
time limit per test
1.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Let's assume that set S consists of m distinct intervals [l1,r1], [l2,r2], ..., [lm,rm] (1≤li≤ri≤n; li,ri are integers).

Let's assume that f(S) is the maximum number of intervals that you can choose from the set S, such that every two of them do not intersect. We assume that two intervals, [l1,r1] and [l2,r2], intersect if there is an integer x, which meets two inequalities: l1≤x≤r1 and l2≤x≤r2.

Sereja wonders, how many sets S are there, such that f(S)=k? Count this number modulo 1000000007 (109+7).

Input

The first line contains integers n, k (1≤n≤500;0≤k≤500).

Output

In a single line, print the answer to the problem modulo 1000000007 (109+7).

Examples
Input
3 1
Output
23
Input
3 2
Output
32
Input
2 0
Output
1
Input
2 2
Output
2

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 1638 题。保留原作者与原赛事署名。