#define IOS ios_base::sync_with_stdio(0); cin.tie(0);

 #include <cstdio>//sprintf islower isupper

 #include <cstdlib>//malloc  exit strcat itoa system("cls")

 #include <iostream>//pair

 #include <fstream>//freopen("C:\\Users\\13606\\Desktop\\草稿.txt","r",stdin);

 #include <bitset>

 //#include <map>

 //#include<unordered_map>

 #include <vector>

 #include <stack>

 #include <set>

 #include <string.h>//strstr substr

 #include <string>

 #include <time.h>//and(((unsigned)time(NULL))); Seed n=rand()%10 - 0~9;

 #include <cmath>

 #include <deque>

 #include <queue>//priority_queue<int, vector<int>, greater<int> > q;//less

 #include <vector>//emplace_back

 //#include <math.h>

 //#include <windows.h>//reverse(a,a+len);// ~ ! ~ ! floor

 #include <algorithm>//sort + unique : sz=unique(b+1,b+n+1)-(b+1);+nth_element(first, nth, last, compare)

 using namespace std;//next_permutation(a+1,a+1+n);//prev_permutation

 #define rint register int

 #define fo(a,b,c) for(rint a=b;a<=c;++a)

 #define fr(a,b,c) for(rint a=b;a>=c;--a)

 #define mem(a,b) memset(a,b,sizeof(a))

 #define pr printf

 #define sc scanf

 #define ls rt<<1

 #define rs rt<<1|1

 typedef long long ll;

 void swapp(int &a,int &b);

 double fabss(double a);

 int maxx(int a,int b);

 int minn(int a,int b);

 int Del_bit_1(int n);

 int lowbit(int n);

 int abss(int a);

 const double E=2.718281828;

 const double PI=acos(-1.0);

 //const ll INF=(1LL<<60);

 const int inf=(<<);

 const double ESP=1e-;

 const int mod=(int)1e9+;

 const int N=(int)5e4+;

 long long C[][];

 void Init() {

     C[][] = ;

     for(int i = ;i <= ;++i) {

         C[i][] = ;

         for(int j = ;j <= i;++j) {

             C[i][j] = (C[i-][j-] + C[i-][j]) % mod;

         }

     }

 }

 //======================================================Cnk预处理;

 ll S[][N],SS[][N],ans[N];

 char s[N];

 void solve()

 {

     ll n,k;

     sc("%lld%lld",&n,&k);

     sc("%s",s);

     for(int i = ;i <= n;++i) S[][i] = ;

     for(int i = ;i <= n;++i) S[][i] = (s[i-]-'') + S[][i-] ;

     for(int i = ;i <= k;++i)

         for(int j = ;j <= n;++j)

             S[i][j] = S[][j] * S[i-][j] % mod;

     SS[][] = ;

     for(int i = ;i <= k;++i) {

         for(int j = ;j <= n;++j)

             SS[i][j] = (SS[i][j-] + S[i][j])%mod;

     }

     for(int i=;i<=n;++i)

     {

         ll sum=;

         for(int j=;j<=k;++j)

         {

             ll temp=C[k][j]*S[k-j][i]%mod*SS[j][i-]%mod;

             if(j&)

                 sum=(sum-temp+mod)%mod;

             else

                 sum=(sum+temp)%mod;

         }

         ans[i]=sum;

     }

     for(int i=;i<=n;++i)

         pr("%lld%c",ans[i],i==n?'\n':' ');

 }

 int main()

 {

     Init();

     int T;

     sc("%d",&T);

     while(T--)solve();

     return ;

 }

 /**************************************************************************************/

 int maxx(int a,int b)

 {

     return a>b?a:b;

 }

 void swapp(int &a,int &b)

 {

     a^=b^=a^=b;

 }

 int lowbit(int n)

 {

     return n&(-n);

 }

 int Del_bit_1(int n)

 {

     return n&(n-);

 }

 int abss(int a)

 {

     return a>?a:-a;

 }

 double fabss(double a)

 {

     return a>?a:-a;

 }

 int minn(int a,int b)

 {

     return a<b?a:b;

 }