SANVI - Sanvi and Magical Numbers

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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

hide comments
Oleg: 2023-10-19 06:38:22

Took 16 WAs to realize that M is not "M non-prime numbers" like description states but "M non-prime digits"

BISHAL GAUTAM: 2017-08-27 19:55:42

Please read the problem statement again. I think problem is easy to understand.

ellaharris873: 2017-08-27 08:55:16

Hello,
I beginner and I do not understand anything yet -:))

Last edit: 2017-08-27 19:54:25

Added by:BISHAL GAUTAM
Date:2017-08-26
Time limit:3s-5s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:https://devskill.com/CodingProblems/ViewProblem/392