Takahashi's Basics in Education and Learning

There is an arithmetic progression with L terms: s_0, s_1, s_2, ... , s_{L-1}.

The initial term is A, and the common difference is B. That is, s_i = A + B \times i holds.

Consider the integer obtained by concatenating the terms written in base ten without leading zeros. For example, the sequence 3, 7, 11, 15, 19 would be concatenated into 37111519. What is the remainder when that integer is divided by M?

Constraints

• All values in input are integers.
• 1 \leq L, A, B < 10^{18}
• 2 \leq M \leq 10^9
• All terms in the arithmetic progression are less than 10^{18}.

Input

Input is given from Standard Input in the following format:

L A B M

Output

Print the remainder when the integer obtained by concatenating the terms is divided by M.

Examples

Input

5 3 4 10007

Output

5563

Input

4 8 1 1000000

Output

891011

Input

107 10000000000007 1000000000000007 998244353

Output

39122908

inputFormat

input are integers.

• 1 \leq L, A, B < 10^{18}
• 2 \leq M \leq 10^9
• All terms in the arithmetic progression are less than 10^{18}.

Input

Input is given from Standard Input in the following format:

L A B M

outputFormat

Output

Print the remainder when the integer obtained by concatenating the terms is divided by M.

Examples

Input

5 3 4 10007

Output

5563

Input

4 8 1 1000000

Output

891011

Input

107 10000000000007 1000000000000007 998244353

Output

39122908

样例

4 8 1 1000000

891011