Crypto

Pesho is crypting a sequence of n numbers where each integer from 1 to n appears exactly once. He is using the following algorithm:

1. Replace each initial number x with the x-th prime number.

2. Choose a random positive integer k, not greater than n.

3. Consider all subsequences with consecutive elements. For each subsequence with at least k elements write down the product of the smallest k numbers.

4. Let p be the number of unique products written in the previous step.

5. The code is "n k p".

Let us see how Pesho should crypt the sequence {4, 1, 3, 2}:

1. The first 4 prime numbers are 2, 3, 5 и 7. In the initial sequence he replaces

• 4 with the fourth prime number which is 7;

• 1 with the first prime number which is 2;

• 3 with the third prime number which is 5;

• 2 with the second prime number which is 3.

Pesho obtains the new sequence 7, 2, 5, 3.

2. He chooses a random number k. Say k = 2.

3. All contiguous subsequences are:{7}, {2}, {5}, {3}, {7, 2}, {2, 5}, {5, 3}, {7, 2, 5}, {2, 5, 3}, {7, 2, 5, 3}

Pesho removes all subsequences with less than k = 2 elements and for each of the rest he computes the product of the smallest k = 2 elements

• {7, 2} 2 * 7 = 14

• {2, 5} 2 * 5 = 10

• {5, 3} 3 * 5 = 15

• {7, 2, 5} 2 * 5 = 10

• {2, 5, 3} 2 * 3 = 6

• {7, 2, 5, 3} 2 * 3 = 6

He writes the numbers {14, 10, 15, 10, 6, 6}

4. There are four unique numbers: {6, 10, 14, 15}, thus p = 4.

5. The code is "4 2 4".

Pesho quickly figured out that the algorithm is much better than he expected. He cannot always decrypt the code unambiguously.

Write a program, which given a code calculates the number of possible initial sequences. Find the answer modulo 1 000 000 007.

Input

One line contains the positive integers n, k (1 ≤ k ≤ n ≤ 400) and p (1 ≤ p ≤ 10^9).

Output

Print the number of possible initial sequences with code "n k p". Print the answer modulo 1 000 000 007.

Examples

Note

In the first example the sequences {1, 3, 2} and {2, 3, 1} can be ctypted as "3 2 3".

In the second example the sequences are {1, 2, 4, 3}, {1, 3, 2, 4}, {1, 4, 2, 3}, {2, 1, 4, 3}, {2, 3, 1, 4}, {2, 4, 1, 3}, {3, 1, 4, 2}, {3, 2, 4, 1}, {3, 4, 1, 2}, {3, 4, 2, 1}, {4, 1, 3, 2}, {4, 2, 3, 1}.