## A Counting Problem 2

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Points: 15
Time limit: 2.0s
Memory limit: 64M

Author:
Problem type

You are given a digit array of length . You must find the number of integers between and (inclusive) satisfying the following condition, modulo :

• The digits for all show up at least once in the integer.

#### Input Specification

The first line will contain the integer .

The next line will contain integers, . It is guaranteed is distinct.

The next line will contain the integer .

#### Output Specification

Output the number of integers satisfying the condition, modulo .

#### 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