A digit string is good if the digits (0-indexed) at even indices are even and the digits at odd indices are prime (2, 3, 5, or 7).
"2582" is good because the digits (2 and 8) at even positions are even and the digits (5 and 2) at odd positions are prime. However, "3245" is not good because 3 is at an even index but is not even.Given an integer n, return the total number of good digit strings of length n. Since the answer may be large, return it modulo 109 + 7.
A digit string is a string consisting of digits 0 through 9 that may contain leading zeros.
Example 1:
Input: n = 1 Output: 5 Explanation: The good numbers of length 1 are "0", "2", "4", "6", "8".
Example 2:
Input: n = 4 Output: 400
Example 3:
Input: n = 50 Output: 564908303
Constraints:
1 <= n <= 1015class Solution {
int MOD = 1_000_000_007;
public int countGoodNumbers(long n) {
long oddPosns = n / 2;
long evenPosns = (n & 1) == 1 ? oddPosns + 1 : oddPosns;
return (int) ((moduloPower(5, evenPosns) * moduloPower(4, oddPosns)) % MOD);
}
private long moduloPower(int base, long exp) {
long res = 1;
while (exp-- > 0)
res = (res * base) % MOD;
return res;
}
}