Yaroslav calls an array of r integers a 1, a 2, ..., a r good, if it meets the following conditions: a 1 - a 2 = 1, a 2 - a 3 = 1, ..., a r - 1 - a r = 1, a r - a 1 = 1, at that . An array of integers b 1, b 2, ..., b r is called great, if it meets the following conditions: The elements in it do not decrease (b i ≤ b i + 1). If the inequalities 1 ≤ r ≤ n and 1 ≤ b i ≤ m hold. If we can rearrange its elements and get at least one and at most k distinct good arrays. Yaroslav has three integers n, m, k . He needs to count the number of distinct great arrays. Help Yaroslav! As the answer may be rather large, print the remainder after dividing it by 1000000007 (109 + 7). Two arrays are considered distinct if there is a position in which they have distinct numbers.

输入描述:

The single line contains three integers n, m, k(1 ≤ n, m, k ≤ 100).

输出描述:

In a single line print the remainder after dividing the answer to the problem by number 1000000007(109 + 7).