Zvonko is playing with digits again, even though his mother has warned him that he is doing too much math and should go outside to play with his friends.

In his latest game, Zvonko looks for multiples of an integer $X$, composed only of certain digits. A multiple of $X$ is any number divisible by $X$.

In order to ruin Zvonko’s fun, his mother decided to get a program that solves the problem. Write a program that calculates how many multiples of $X$ are between $A$ and $B$ (inclusive), such that, when written in decimal, they contain only certain allowed digits.

-----Input-----
The first line of input contains three integers $X$, $A$ and $B$ ($1 \le X < 10^{11}$ , $1 \le A \le B < 10^{11}$). The second line contains the allowed digits. The digits will be given with no spaces, sorted in increasing order and without duplicates. There will be at least one allowed digit.

-----Output-----
Output the number of multiples Zvonko can make on a single line.

-----Examples-----
Sample Input 1:
2 1 20
0123456789
Sample Output 1:
10

Sample Input 2:
6 100 9294
23689
Sample Output 2:
111

Source: kattis | Difficulty: HARD


Solutions: