#include <bits/stdc++.h>
#define LOG(FMT...) fprintf(stderr, FMT);
#define rep(i, j, k) for(int i = j; i <= k; ++ i)
#define per(i, j, k) for(int i = j; i >= k; -- i)
using namespace std;

#define fs first
#define sc second
#define pb push_back
#define mp make_pair

using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;

const int N = 50;
const int mod = 1e9 + 7;

int qpow(int a, int b) {
  int ans = 1;
  for(; b >= 1; b >>= 1, a = (ll)a * a % mod)
    if(b & 1) ans = (ll)ans * a % mod;
  return ans;
}

namespace ITPL { //O(n^2) Interpolation

vi inter(vi x, vi y) { //in mod
  assert(x.size() == y.size());
  int n = int(x.size()) - 1; //x, y [0, n]
  // rep(i, 0, n) { printf("f(%d) = %d\n", x[i], y[i]); }
  vi p(1, 1);
  rep(i, 0, n) {
    p.pb(0);
    per(j, i + 1, 0) {
      p[j] = ((ll)p[j] * (-x[i]) + (j ? p[j-1] : 0)) % mod;
    }
  }
  vi res(n + 1);
  rep(i, 0, n) {
    vi q(n + 1);
    int z = 1;
    rep(j, 0, n) if(j != i)
      z = (ll)z * (x[i] - x[j]) % mod;
    z = (ll)y[i] * qpow(z, mod-2) % mod;
    q[n] = 1;
    per(j, n, 1)
      q[j-1] = (p[j] + (ll)q[j] * x[i]) % mod;
    rep(j, 0, n)
      res[j] = (res[j] + (ll)z * q[j]) % mod;
  }
  rep(i, 0, n)
    if(res[i] < 0)
      res[i] += mod;
  return res;
}
void Test() {
  //y = 10 x^3 + 5 x^2 - x + 2
  vi v1 = {0, 1, 2, 5}, v2;
  for(int x: v1) v2.pb((10 * x * x * x + 5 * x * x - x + 2 + mod) % mod);
  vi res = inter(v1, v2);
  for(int x: res)
    printf("%d ", x);
  puts("");
}

}

int n, k, p[6], sufp[6];
int f[5][N], c[N][N], g[N][N], fac[N], fav[N], e1[N][N], e0[N][N], pw[5 * N];
void upd(int &x, ll y) {
  x = (x + y) % mod;
}
int solve(int x0) {
  pw[0] = 1;
  rep(i, 1, (k-1) * n)
    pw[i] = (ll)pw[i-1] * x0 % mod;
  f[0][1] = 1;
  rep(t, 1, k) {
    rep(i, 0, n)
      rep(j, 1, n - i) {
        int c = i * j;
        e0[i][j] = qpow((sufp[t+1] + p[0]) % mod, c);
        e1[i][j] = (qpow((p[0] + sufp[t]) % mod, c) - e0[i][j]) % mod;
        // printf("e%d %d = %d %d\n", i, j, e0[i][j], e1[i][j]);
      }

    rep(s, 1, n)
      rep(i, 0, n-s)
        g[s][i] = !i;
    rep(d, 1, n) {
      // printf("d = %d\n", d);
      f[t][d] = 0;
      rep(i, 1, d)
        upd(f[t][d], (ll)f[t-1][i] * g[i][d-i] % mod * c[d-1][i-1]);
      per(i, n, d) {//g[s][i]
        rep(s, 1, n-i) {
          int t1 = 1, _t3 = 1, t3 = 1;
          rep(k, 1, i / d) {
            // printf("d = %d, i = %d, k = %d\n",  d, i, k);
            // assert(f[t][d]);
            t1 = (ll)t1 * fav[d] % mod * e1[s][d] % mod * f[t][d] % mod; //d < z
            t3 = (ll)t3 * _t3 % mod; //pow(e0[d][d], k*(k-1)/2 = 0 + 1 + .. + k-1)
            _t3 = (ll)_t3 * e0[d][d] % mod; //pow(e0[d][d], k)
            //f: d < s+i
            // ll tt = (ll)g[s][i - k*d] * pw[(t-1)*k] % mod
              // * fac[i] % mod * fav[k] % mod * fav[i-k*d] % mod * e0[i - k*d][k*d] % mod * t1 % mod * t3;
            // cout << ((tt+mod) % mod) << endl;
            upd(g[s][i], (ll)g[s][i - k*d] * pw[(t-1)*k] % mod
              * fac[i] % mod * fav[k] % mod * fav[i-k*d] % mod * e0[i - k*d][k*d] % mod * t1 % mod * t3);
          }
        }
      }
      
      // rep(i, 1, n-s)
        // printf("g%d %d = %d\n", s, i, (g[s][i] + mod)%mod);
    }
  }
  return f[k][n];
}


int main() {

  rep(i, 0, N-1) {
    c[i][0] = 1;
    rep(j, 1, i)
      c[i][j] = (c[i-1][j-1] + c[i-1][j]) % mod;
  }
  *fac = 1;
  rep(i, 1, N-1) fac[i] = (ll)fac[i-1] * i % mod;
  fav[N-1] = qpow(fac[N-1], mod-2);
  per(i, N-1, 1) fav[i-1] = (ll)fav[i] * i % mod;
  // Test();
  const int i100 = qpow(100, mod-2);
  int test;
  scanf("%d", &test);
  rep(T, 1, test) {
    scanf("%d%d", &n, &k);
    rep(i, 0, k) scanf("%d", p + i), p[i] = (ll)p[i] * i100 % mod;
    sufp[k+1] = 0;
    per(i, k, 0) sufp[i] = (sufp[i+1] + p[i]) % mod;
    vi x((k - 1) * (n - 1) + 1);
    iota(x.begin(), x.end(), 0);
    vi y;
    for(int x0: x) y.pb(solve(x0));
    
    vi res = ITPL::inter(x, y);
    int o = res.size();
    for(int z: res) {
      printf("%d%c", z, " \n"[!--o]);
    }
  }
  return 0;
}