#include<bits/stdc++.h>
#define x first
#define y second
#define PB push_back
#define mst(x,a) memset(x,a,sizeof(x))
#define all(a) begin(a),end(a)
#define rep(x,l,u) for(ll x=l;x<u;x++)
#define rrep(x,l,u) for(ll x=l;x>=u;x--)
#define sz(x) x.size()
#define IOS ios::sync_with_stdio(false);cin.tie(0);
using namespace std;
typedef unsigned long long ull;
typedef pair<int,int> PII;
typedef pair<char,char> PCC;
typedef long long ll;
typedef pair<ll,ll> PLL;
const int N=1e5+10;
const int M=1e6+10;
const int INF=0x3f3f3f3f;
const int mod=1e9+7;
void solve(){
int a,b;cin>>a>>b;
string s;cin>>s;
int ans=0,cnt=10000;
rep(i,0,sz(s)){
if(s[i]=='1'){
ans+=min(a,cnt*b);
cnt=0;
}else cnt++;
}
cout<<ans<<endl;
}
int main(){
IOS;
#ifdef dejavu
freopen("test.txt", "r", stdin);
freopen("test.txt", "w", stdout);
#endif // dejavu
int t;cin>>t;
while(t--)
solve();
return 0;
}