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#include <cstdio>
#include <iostream>
#include <vector>

using namespace std;

const int kDi[5] = { 1, 0, -1,  0, 0 };
const int kDj[5] = { 0, 1,  0, -1, 0 };
const int kModulus = 1000 * 1000 * 1000 + 7;

void Normalize(long long* a) {
  (*a) %= kModulus;
}

void AddTo(long long a, long long* b) {
  Normalize(&a);
  Normalize(b);
  (*b) += a;
  Normalize(b);
}

void MultiplyBy(long long a, long long* b) {
  Normalize(&a);
  Normalize(b);
  (*b) *= a;
  Normalize(b);
}

long long Choose(const long long a, long long b) {
  vector<long long> n;
  for (int i = 0; i < b; ++i) n.push_back(a - i);
  while (b > 0) {
    for (int i = 0; i < n.size(); ++i) if (n[i] % b == 0) {
      n[i] /= b;
      break;
    }
    --b;
  }
  long long ret = 1;
  for (int i = 0; i < n.size(); ++i) MultiplyBy(n[i], &ret);
  return ret;
}

vector<vector<pair<int, int> > > piece_parts;
vector<vector<vector<bool> > > piece_masks;

void LearnPiece(const string& s1, const string& s2, const string& s3, const string& s4) {
  piece_parts.resize(piece_parts.size() + 1);
  for (int i = 0; i < s1.size(); ++i) if (s1[i] == 'x') piece_parts.back().push_back(make_pair(0, i));
  for (int i = 0; i < s2.size(); ++i) if (s2[i] == 'x') piece_parts.back().push_back(make_pair(1, i));
  for (int i = 0; i < s3.size(); ++i) if (s3[i] == 'x') piece_parts.back().push_back(make_pair(2, i));
  for (int i = 0; i < s4.size(); ++i) if (s4[i] == 'x') piece_parts.back().push_back(make_pair(3, i));
  piece_masks.resize(piece_masks.size() + 1);
  int x_max = 0, y_max = 0;
  for (int i = 0; i < piece_parts.back().size(); ++i) {
    x_max = max(x_max, piece_parts.back()[i].first );
    y_max = max(y_max, piece_parts.back()[i].second);
  }
  piece_masks.back().resize(x_max + 5, vector<bool>(y_max + 5));
  for (int i = 0; i < piece_parts.back().size(); ++i) for (int d = 0; d <= 4; ++d) {
    piece_masks.back()[kDi[d] + 2 + piece_parts.back()[i].first][kDj[d] + 2 + piece_parts.back()[i].second] = true;
  }
}

void LearnPiece(const string& s1, const string& s2, const string& s3) {
  LearnPiece(s1, s2, s3, "");
}

void LearnPiece(const string& s1, const string& s2) {
  LearnPiece(s1, s2, "");
}

void LearnPiece(const string& s1) {
  LearnPiece(s1, "");
}

void LearnPieces() {
  // 0
  LearnPiece("xx");

  // 1
  LearnPiece("x",
             "x");

  // 2
  LearnPiece("xxx");

  // 3
  LearnPiece("x",
             "x",
             "x");

  // 4
  LearnPiece("xx",
             "x ");

  // 5
  LearnPiece("xx",
             " x");

  // 6
  LearnPiece("x ",
             "xx");

  // 7
  LearnPiece(" x",
             "xx");

  // 8
  LearnPiece("xxxx");

  // 9
  LearnPiece("x",
             "x",
             "x",
             "x");

  // 10
  LearnPiece("xxx",
             "  x");

  // 11
  LearnPiece("x  ",
             "xxx");

  // 12
  LearnPiece("xx",
             "x ",
             "x ");

  // 13
  LearnPiece(" x",
             " x",
             "xx");

  // 14
  LearnPiece("  x",
             "xxx");

  // 15
  LearnPiece("xxx",
             "x  ");

  // 16
  LearnPiece("xx",
             " x",
             " x");

  // 17
  LearnPiece("x ",
             "x ",
             "xx");

  // 18
  LearnPiece("xxx",
             " x ");

  // 19
  LearnPiece(" x ",
             "xxx");

  // 20
  LearnPiece(" x",
             "xx",
             " x");

  // 21
  LearnPiece("x ",
             "xx",
             "x ");

  // 22
  LearnPiece("xx ",
             " xx");

  // 23
  LearnPiece(" x",
             "xx",
             "x ");

  LearnPiece("x ",
             "xx",
             " x");

  LearnPiece("xx",
             "xx");
}

int GetPieceCount() {
  return piece_parts.size();
}

int GetPieceSize(const int k) {
  return piece_parts[k].size();
}

vector<vector<int> > dist;

bool PieceFits(const int x, const int y, const int k) {
  bool one_found = false, two_found = false;
  for (int i = 0; i < piece_parts[k].size(); ++i) {
    const int ii = x + piece_parts[k][i].first;
    const int jj = y + piece_parts[k][i].second;
    if (dist[ii][jj] == 0) return false;
    if (dist[ii][jj] == 3) return false;
    if (dist[ii][jj] == 1) one_found = true;
    if (dist[ii][jj] == 2) two_found = true;
  }
  return one_found && two_found;
}

vector<vector<long long> > ways;

void ComputePieceDeltas(int x, int y, const int k, long long* C1, long long* W2) {
  x -= 2;
  y -= 2;
  *C1 = 0;
  *W2 = 0;
  for (int i = 0; i < piece_masks[k].size(); ++i) for (int j = 0; j < piece_masks[k][i].size(); ++j) if (piece_masks[k][i][j]) {
    const int ii = x + i;
    const int jj = y + j;
    // cerr << "masked " << ii << " " << jj << endl;
    if (dist[ii][jj] == 2) *W2 += ways[ii][jj];
    else if (dist[ii][jj] == 1) {
      ++*C1;
      for (int d = 0; d < 4; ++d) if (!piece_masks[k][i + kDi[d]][j + kDj[d]]) {
        const int iii = ii + kDi[d];
        const int jjj = jj + kDj[d];
        if (dist[iii][jjj] == 2) ++*W2;
      }
    }
    // cerr << *C1 << ' ' << *W2 << endl;
  }
}

int n;
vector<long long> answer;

void ComputeStats() {
  long long C1 = 0, W2 = 0;
  for (int i = 1; i <= n; ++i) for (int j = 1; j <= n; ++j) {
    if (dist[i][j] == 1) ++C1;
    if (dist[i][j] == 2) W2 += ways[i][j];
  }

  answer.resize(6);
  for (int i = 0; i <= 5; ++i) AddTo(Choose(C1, i), &answer[i]);

  // cerr << "Fitting pieces" << endl;

  for (int i = 1; i <= n; ++i) for (int j = 1; j <= n; ++j) for (int k = 0; k < GetPieceCount(); ++k) if (PieceFits(i, j, k)) {
    // cerr << k << " fits at " << i << ' ' << j << endl;
    const int size = GetPieceSize(k);
    // cerr << "piece size " << size << endl;
    AddTo(1, &answer[size]);
    if (size < 4) {
      long long C1_delta, W2_delta;
      ComputePieceDeltas(i, j, k, &C1_delta, &W2_delta);
      // cerr << "deltas " << C1_delta << ' ' << W2_delta << endl;
      AddTo(       C1 - C1_delta    , &answer[size + 1]);
      AddTo(Choose(C1 - C1_delta, 2), &answer[size + 2]);
      AddTo(       W2 - W2_delta    , &answer[size + 2]);
    }
    // cerr << "answers";
    // for (int i = 0; i < 5; ++i) cerr << ' ' << answer[i];
    // cerr << endl;
  }
}

void Spread(const int s) {
  for (int i = 1; i <= n; ++i) for (int j = 1; j <= n; ++j) if (dist[i][j] == s) for (int d = 0; d < 4; ++d) {
    const int ii = i + kDi[d];
    const int jj = j + kDj[d];
    if (dist[ii][jj] == -1) dist[ii][jj] = s + 1;
    if (dist[ii][jj] == s + 1) ways[ii][jj] += ways[i][j];
  }
}

int main() {
  LearnPieces();

  int k;
  scanf("%d%d", &n, &k);

  dist.resize(n + 5, vector<int>(n + 5, 3));
  ways.resize(n + 5, vector<long long>(n + 5));

  for (int i = 1; i <= n; ++i) for (int j = 1; j <= n; ++j) {
    char c;
    do { scanf("%c", &c); } while (c != '#' && c != '.');
    if (c == '#') {
      dist[i][j] = 0;
    } else {
      dist[i][j] = -1;
    }
  }

  Spread(0);
  for (int i = 1; i <= n; ++i) for (int j = 1; j <= n; ++j) if (dist[i][j] == 1) ways[i][j] = 1;
  Spread(1);
  ComputeStats();

  printf("%lld\n", answer[k]);

  return 0;
}