Largest Adjacent-Digit Product

Take every contiguous window of span digits and multiply its digits. Return the largest product. Leading zeros are ordinary digits; a window containing zero has product zero. Do not reorder or skip digits.

Implement largest_adjacent_digit_product(digits, span).

Input

digits: The digit sequence, including any leading zeros.

span: The exact number of adjacent digits in a window.

Output

Return the greatest product over all windows of this width.

Constraints

1 ≤ digit-string length ≤ 100,000. Characters are 0…9. 1 ≤ span ≤ min(18, length). All products fit signed 64-bit.

Examples

Input:
span = 2
digits = "23405"

Expected output:
expected = 12

Input:
long long span = 2;
std::string digits = "23405";

Expected output:
long long expected = 12;

Input:
long span = 2;
string digits = "23405";

Expected output:
long expected = 12;

Input:
span = 3
digits = "102"

Expected output:
expected = 0

Input:
long long span = 3;
std::string digits = "102";

Expected output:
long long expected = 0;

Input:
long span = 3;
string digits = "102";

Expected output:
long expected = 0;

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

• Exercism: Largest Series Product