The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Codeforces Round 182 (Div. 1) |
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Finished |

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E. Yaroslav and Arrangements

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYaroslav 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 (10^{9} + 7).

Two arrays are considered distinct if there is a position in which they have distinct numbers.

Input

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

Output

In a single line print the remainder after dividing the answer to the problem by number 1000000007 (10^{9} + 7).

Examples

Input

1 1 1

Output

0

Input

3 3 3

Output

2

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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