Numbers of length N and value less than K

Problem Description

Given a set of digits (A) in sorted order, find how many numbers can be formed using these digits such that its length is B and whose value is less than the number C.

NOTE: All numbers can only have digits from the given set.

Problem Constraints

0 <= |A| <= 10
1 <= B <= 9
0 <= C <= 1e9
0 <= A[i] <= 9

Input Format

The first argument is an integer array A.
The second argument is an integer B.
The third argument is an integer C.

Output Format

Return an integer.

Example Input

Input 1:

A = [0, 1, 5]
B = 1
C = 2

Input 2:

A = [0, 1, 2, 5]
B = 2
C = 21

Example Output

Output 1:

Output 2:

Example Explanation

Explanation 1:

0 and 1 are possible

Explanation 2:

10, 11, 12, 15, 20 are possible

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.

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Numbers of length N and value less than K

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