Problem:
Score : 400 points

Problem Statement

Given is a string S. Each character in S is either a digit (0, ..., 9) or ?.

Among the integers obtained by replacing each occurrence of ? with a digit, how many have a remainder of 5 when divided by 13? An integer may begin with 0.

Since the answer can be enormous, print the count modulo 10^9+7.

Constraints

S is a string consisting of digits (0, ..., 9) and ?.

1 \leq |S| \leq 10^5

Input

Input is given from Standard Input in the following format:

S

Output

Print the number of integers satisfying the condition, modulo 10^9+7.

Sample Input 1

??2??5

Sample Output 1

768

For example, 482305, 002865, and 972665 satisfy the condition.

Sample Input 2

?44

Sample Output 2

1

Only 044 satisfies the condition.

Sample Input 3

7?4

Sample Output 3

0

We may not be able to produce an integer satisfying the condition.

Sample Input 4

?6?42???8??2??06243????9??3???7258??5??7???????774????4?1??17???9?5?70???76???

Sample Output 4

153716888

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<stdint.h>
#include<inttypes.h>
#include<string.h>

typedef int32_t i32;
typedef int64_t i64;

#define ALLOC(size,type) ((type*)calloc((size),sizeof(type)))

void run (void) {
  char *s = ALLOC (100000 + 1, char);
  scanf ("%s", s);
  const i32 p = 13;
  i64 *dp = ALLOC (p, i64);
  i64 *next = ALLOC (p, i64);
  dp[0] = 1;
  const i32 mod = 1000000007;
  for (i32 i = 0; s[i] != '\0'; ++i) {
    memset (next, 0, sizeof (i64) * p);
    if (s[i] != '?') {
      i32 d = s[i] - '0';
      for (i32 j = 0; j < p; ++j) {
        next[(10 * j + d) % p] += dp[j];
      }
    } else {
      for (i32 d = 0; d < 10; ++d) {
        for (i32 j = 0; j < p; ++j) {
          next[(10 * j + d) % p] += dp[j];
        }
      }
    }
    for (i32 j = 0; j < p; ++j) {
      dp[j] = next[j] % mod;
    }
  }
  printf ("%" PRIi64 "\n", dp[5]);
}

int main (void) {
  run();
  return 0;
}