#pragma GCC optimize("Ofast","inline")
#include <bits/stdc++.h>
#define clr(x) memset(x,0,sizeof (x))
#define fi first
#define se second
using namespace std;
typedef long long LL;
LL read(){LL x=0,f=0;char ch=getchar();while (!isdigit(ch))f|=ch=='-',ch=getchar();while (isdigit(ch))x=(x<<1)+(x<<3)+(ch^48),ch=getchar();return f?-x:x;
}
const int N=500005;
const LL INF=2e18;
int T,n,m;
LL w;
int Fail[N],nf[N];
struct brd{int v,d,c;
}b[N];
char s[N];
LL dis[N],rng;
LL gcd(LL a,LL b){return b?gcd(b,a%b):a;
}
void Trans(LL nr){static LL d[N];for (int i=0;i<nr;i++)d[i]=INF;for (int i=0;i<rng;i++)d[dis[i]%nr]=min(d[dis[i]%nr],dis[i]);int g=gcd(rng,nr);for (int t=0;t<g;t++){int e=nr/g*2,_i=t,rg=rng%nr;for (LL i=t,j=0;j<e;i+=rng,j++){d[_i]=min(d[_i],d[_i<rg?_i-rg+nr:_i-rg]+rng);if ((_i+=rg)>=nr)_i-=nr;}}rng=nr;for (int i=0;i<rng;i++)dis[i]=d[i];
}
pair <LL,LL> Q[N*2];
int head,tail;
void DP(int d,int c){int g=gcd(rng,d);for (int t=0;t<g;t++){head=1,tail=0;int e=rng/g*2,_i=t;for (LL i=t,j=0;j<e;i+=d,j++){if (head<=tail&&Q[head].fi+(LL)c*d<=i)head++;if (head<=tail)dis[_i]=min(dis[_i],Q[head].se+rng+i);while (head<=tail&&Q[tail].se>=dis[_i]-i)tail--;Q[++tail]=make_pair(i,dis[_i]-i);if ((_i+=d)>=rng)_i-=rng;}}
}
int main(){T=read();while (T--){n=read(),w=read();scanf("%s",s+1);Fail[1]=0;for (int i=2;i<=n;i++){int k=Fail[i-1];while (k>0&&s[k+1]!=s[i])k=Fail[k];if (s[k+1]==s[i])k++;Fail[i]=k;}m=0;for (int i=n;i>0;i=Fail[i])nf[Fail[i]]=i;for (int j=0;j<n;j=nf[j]){int i=n-j;if (j==0)m++,b[m].v=i,b[m].d=0,b[m].c=1;else if (!b[m].d)b[m].d=b[m].v-i,b[m].c++,b[m].v=i;else if (b[m].v-b[m].d==i)b[m].v=i,b[m].c++;elsem++,b[m].v=i,b[m].d=0,b[m].c=1;}if (!b[m].d)b[m].d=1;clr(dis);rng=n;for (int i=0;i<n;i++)dis[i]=INF;dis[0]=n;for (int i=1;i<=m;i++){Trans(b[i].v);DP(b[i].d,b[i].c);}LL ans=0;for (int i=0;i<rng;i++)if (dis[i]<=w)ans+=w/rng-dis[i]/rng+(w%rng>=dis[i]%rng?1:0);cout<<ans<<endl;}return 0;
}