Let us define a Magical number as a positive integer number which meets the following criteria on its representation:

1. It does not contain any zeros.
2. Each digits may appears at most twice in it.
3. The absolute differences between summation of count of non-prime digits and count of prime-digits do not exceed K.

Sanvi likes numbers which are not prime. So, she wants to allow at most M non-prime numbers to violate the rule number-2. Sanvi also uses following algorithm in rule number-3 to calculate count of each digit d in a number:

      count(d) = min(total occurrences of d in number, 2)

You are given an integer number N. Your task is to find the total Magical numbers in the range from 1 to N following Sanvi's command. Since the answer could be very large, print it modulo 10^9+7.

Input

Input contains several test cases up to EOF (End Of File), which contains three space separated integers N (1 ≤ N ≤ 10^18), K (0 ≤ K ≤ 18) and M (0 ≤ M ≤ 5) as described in the problem statement. Total test cases will not exceed 5.

Output

Output a single integer denoting the total Magical numbers from 1 to N following Sanvi's command. Since the answer could be very large print it modulo 10^9+7.

Example

Input:
10 1 0
5 3 2

Output:
9
5