for i in range(int(input())):
a ,b = map(int , input().split())
s = (input())
ind = []
for j in range(len(s)):
if s[j]=="1":
ind.append(j+1)
var = []
for j in range(len(ind)-1):
if ind[j+1]-ind[j]!=1:
var.append(ind[j+1]-ind[j]-1)
answer = []
ans = 0
for j in range(len(var)):
if var[j]*b <= a:
ans += var[j]*b
else:
answer.append(ans+a)
ans = 0
if j==len(var)-1:
answer.append(ans+a)
if s.count("1")==0:
print(0)
elif len(answer)==0:
print(a)
else:
print(sum(answer))#include <bits/stdc++.h>
using namespace std;
int dp[100005],z[100005];
char c[10005];
int main()
{
int t;
cin>>t;
while(t--){
//TODO
int a,b;
memset(dp,0,sizeof(dp));
cin>>a>>b>>c;
int n=strlen(c);
if(c[0]=='1'){
//TODO
dp[0]=a;
}
for(int i=0; i<n; i++){
//TODO
if(c[i]=='0'){
//TODO
dp[i]=dp[i-1];
}
else{
int j;
for(j=i-1; j>=0; j--){
//TODO
if(c[j]=='1'){
//TODO
break;
}
}
if(j<0){
//TODO
dp[i]=a;
continue;
}
if(c[i-1]=='1'){
//TODO
dp[i]=dp[i-1];
continue;
}
dp[i]=min(dp[i-1]+a,dp[j]+(i-j-1)*b);
}
}
cout<<dp[n-1]<<endl;
}
return 0;
}
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