681B.cpp

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*/                              
#include<bits/stdc++.h>
using namespace std;
 
#define fastio ios_base::sync_with_stdio(0); cin.tie(0)
#define LL long long 
#define mod 1000000007 
#define all(v) v.begin(),v.end()
#define pr(v) pair<v,v>
#define pb push_back
#define FOR(i, j, k) for (auto i=j ; i<k ; i++)
#define ROF(i, j, k) for (auto i=j ; i>=k ; i--) 
#define debug(...) fprintf(stderr, __VA_ARGS__), fflush(stderr)
#define time__(d) for(long blockTime = 0; (blockTime == 0 ? (blockTime=clock()) != 0 : false); debug("%s time : %.4fs", d, (double)(clock() - blockTime) / CLOCKS_PER_SEC))

const long long INF = 1e18;
const long long MAX = 2e5+10;
int main(){
    fastio;
    int t=1; cin>>t;
    while(t--){
        int a,bb; cin>>a>>bb;
        string s; cin>>s;
        int c=0,b=0;
        int i = 0,n=s.size();
        vector<int> y;
        ROF(i,s.size()-1,0) if(s[i]=='0') s.pop_back(); else break;
        while(i<n && s[i]=='0') i++;
        n=s.size();

        while(i<n) {
            int ct=0;
            while(i<n && s[i]=='1') i++,ct++;
            if(ct) c+=a; ct=0;
            while(i<n && s[i]=='0') i++,ct++;
            if(ct) y.push_back(ct);
        }i=0; sort(all(y));
        int ans = c; 
        while(i<y.size()){
            c = c-a+bb*y[i]; //  cout<<y[i]<<" ";
            ans = min(ans,c);
            i++;
        }
       // c+=bb*y[i];
        ans = min(ans,c);
        cout<<ans<<"\n";        
    }
}