#include <bits/stdc++.h>
using namespace std;
template <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c* x) -> decltype(cerr << *x, 0);
template <class c>
char dud(...);
struct debug {
  template <class c>
  debug& operator<<(const c&) {
    return *this;
  }
};
vector<char*> tokenizer(const char* args) {
  char* token = new char[111];
  strcpy(token, args);
  token = strtok(token, ", ");
  vector<char*> v({token});
  while (token = strtok(NULL, ", ")) v.push_back(token);
  return reverse(v.begin(), v.end()), v;
}
void debugg(vector<char*> args) { cerr << "\b\b "; }
template <typename Head, typename... Tail>
void debugg(vector<char*> args, Head H, Tail... T) {
  debug() << " [" << args.back() << ": " << H << "] ";
  args.pop_back();
  debugg(args, T...);
}
long long mod = 1e9 + 7;
const int MX = 0x3f3f3f3f;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t;
  cin >> t;
  while (t--) {
    int a, b, i, prev = -1;
    cin >> a >> b;
    string s;
    cin >> s;
    vector<int> v;
    long long ans = 0;
    for (i = 0; i <= (int)s.size() - 1; i++) {
      if (s[i] == '1') {
        if (prev != -1 && (i - prev - 1) * b < a)
          ans += (i - prev - 1) * b;
        else
          ans += a;
        prev = i;
      }
    }
    cout << ans << "\n";
  }
  return 0;
}
