We are going to consider subsets $ P $ of a given set $\{1, \ldots, n\}$. We are interested in subsets such that for a given natural number $ x > 1 $ and for any natural number $ y $ at least one of the numbers $ y $, $ x \cdot y $ doesn't belong to $ P $. We would like to calculate the number of such subsets, that have exactly $ k $ elements. It is possible that the number of such subsets is huge - therefore it is sufficient to calculate the remainder of the division of the result by $ m $.
Write a program which:
- reads from the standard input four integers: $ n $, $ m $, $ k $ and $ x $,
- calculates the remainder of the division by $ m $ of the number of $ k $-element subsets of set $\{1, \ldots, n\}$, that fulfill the requirements described above,
- writes result to the standard output.
Input Format
In the first and only line of the standard input there are four integers $ n $, $ m $, $ k $ and $ x $ ($1 ≤ n ≤ 10^{18}$, $2 ≤ m ≤ 1\,000\,000$, $0 ≤ k ≤ 1\,000$, $2 ≤ x ≤ 10$), separated by single spaces.
Output Format
The first and only line should contain one integer - the reminder of the division by $ m $ of the number of $ k $-element subsets of set $\{1, \ldots, n\}$ that fulfill the specified requirements.
Example
Input
6 1234 3 2
Output
9
Notes
Considered subsets are: {1, 3, 4}, {1, 3, 5}, {1, 4, 5}, {1, 4, 6}, {1, 5, 6}, {2, 3, 5}, {2, 5, 6}, {3, 4, 5} and {4, 5, 6}.