A Digit Problem

View as PDF
Submit solution
Points: 12 (partial)
Time limit: 1.0s
Memory limit: 64M
Author:
Ninjaclasher
Problem type

You are given a digit array a of length N. You must find the number of integers between 0 and K (inclusive) satisfying the following condition, modulo 10^9+7:

  • The digits a_i for all i (1 \le i \le N) show up at least once in the integer.

Input Specification

The first line will contain the integer N (1 \le N \le 10).

The next line will contain N integers, a_i (0 \le a_i \le 9). It is guaranteed a_i is distinct.

The next line will contain the integer K (0 \le K < 10^{1000}).

Output Specification

Output the number of integers satisfying the condition, modulo 10^9+7.

Sample Input 1

1
1
11

Sample Output 1

3

Explanation For Sample 1

The three integers satisfying the constraints are:

  • 1
  • 10
  • 11

Sample Input 2

5
3 9 2 0 1
512309002821093

Sample Output 2

891474356

Comments


  • 0
    maxcruickshanks  commented on Dec. 6, 2024, 2:27 a.m.

    Since the original data were weak, an additional test case was added, and all submissions were rejudged. Data were provided by dnialh_.


  • 7
    ross_cleary  commented on June 15, 2020, 6:58 p.m.

    Remember that leading zeros do not count.