#include <bits/stdc++.h>
using namespace std;
int main() {
  long long int n, m, k, t, sum = 0, a, b, p;
  cin >> t;
  while (t--) {
    bool fg = 0;
    p = 0;
    k = 0;
    sum = 0;
    cin >> a >> b;
    string s;
    cin >> s;
    n = s.size();
    for (long long int i = 0; i <= n - 1; i++) {
      if (s[i] == '1') {
        if (fg == 0) {
          p += a;
          fg = 1;
          k = 0;
        } else if (k > 0) {
          p += min(k * b, a);
          k = 0;
          continue;
        }
      } else
        k++;
    }
    cout << p << endl;
  }
  return 0;
}
