Division by Two with Something

Given are integers N and X. For each integer k between 0 and X (inclusive), find the answer to the following question, then compute the sum of all those answers, modulo 998244353.

• Let us repeat the following operation on the integer k. Operation: if the integer is currently odd, subtract 1 from it and divide it by 2; otherwise, divide it by 2 and add 2^{N-1} to it. How many operations need to be performed until k returns to its original value? (The answer is considered to be 0 if k never returns to its original value.)

Constraints

• 1 \leq N \leq 2\times 10^5
• 0 \leq X < 2^N
• X is given in binary and has exactly N digits. (In case X has less than N digits, it is given with leading zeroes.)
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N X

Output

Print the sum of the answers to the questions for the integers between 0 and X (inclusive), modulo 998244353.

Examples

Input

3 111

Output

40

Input

6 110101

Output

616

Input

30 001110011011011101010111011100

Output

549320998

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N X

outputFormat

Output

Print the sum of the answers to the questions for the integers between 0 and X (inclusive), modulo 998244353.

Examples

Input

3 111

Output

40

Input

6 110101

Output

616

Input

30 001110011011011101010111011100

Output

549320998

样例

30
001110011011011101010111011100

549320998