#include <bits/stdc++.h>
using namespace std;
template <class C>
void mini(C& a4, C b4) {
  a4 = min(a4, b4);
}
template <class C>
void maxi(C& a4, C b4) {
  a4 = max(a4, b4);
}
template <class T1, class T2>
ostream& operator<<(ostream& rout, pair<T1, T2> pair) {
  return rout << "(" << pair.first << ", " << pair.second << ")";
}
const int P = 10007;
const int MN = 201;
vector<int> T[MN][MN];
vector<int> pw;
int rev[P];
const int S = 26;
int pot(int x, int n) {
  int res = 1;
  while (n) {
    if (n & 1) res = (res * x) % P;
    x = (x * x) % P;
    n >>= 1;
  }
  return res;
}
int gauss(vector<vector<int> >& a, vector<int>& res) {
  int n = a.size(), m = a[0].size() - 1;
  res.resize(m);
  for (__typeof((res).begin()) i = ((res).begin()); i != (res).end(); ++i)
    *i = 0;
  vector<int> wyb(n, -1);
  for (int j = 0; j < (m); ++j) {
    for (int i = 0; i < (n); ++i)
      if (a[i][j] != 0 && wyb[i] == -1) {
        wyb[i] = j;
        if (a[i][j] < 0) a[i][j] += P;
        int odw = rev[a[i][j]];
        for (int jj = 0; jj < (m + 1); ++jj) a[i][jj] = (a[i][jj] * odw) % P;
        for (int ii = 0; ii < (n); ++ii)
          if (i != ii && a[ii][j] != 0) {
            int wsp = a[ii][j];
            for (int jj = 0; jj < (m + 1); ++jj)
              a[ii][jj] = (a[ii][jj] - wsp * a[i][jj]) % P;
          }
        break;
      }
  }
  int dim = m - n;
  for (int i = 0; i < (n); ++i)
    if (wyb[i] == -1) {
      dim++;
      if (a[i][m] != 0) return -1;
    } else
      res[wyb[i]] = a[i][m];
  for (__typeof((res).begin()) i = ((res).begin()); i != (res).end(); ++i)
    if (*i < 0) *i += P;
  return dim;
}
vector<int> solve(vector<int> vals, int n) {
  int M = 2 * n + 1;
  vector<vector<int> > A(M, vector<int>(M + 1, 0));
  for (int j = 0; j < (3); ++j) {
    A[0][j] = 1;
    for (int _ = 0; _ < (n); ++_) A[0][j] = (A[0][j] * (S - j)) % P;
  }
  for (int i = (1); i <= (M - 1); ++i)
    for (int j = 0; j < (3); ++j) A[i][j] = (A[i - 1][j] * (S - j)) % P;
  for (int i = 0; i < (M); ++i) {
    for (int j = (3); j <= (M - 1); ++j) A[i][j] = (A[i][j - 2] * (n + i)) % P;
  }
  for (int i = 0; i < (M); ++i) A[i][M] = vals[i + n];
  vector<int> res(M);
  int dim = gauss(A, res);
  assert(dim != -1);
  return res;
}
int main() {
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(10);
  for (int i = 0; i < (P); ++i) rev[i] = pot(i, P - 2);
  string s;
  int L;
  cin >> s >> L;
  int n = s.length();
  L += n;
  bool odd = (L % 2 == 1);
  L = (L + 1) / 2;
  int mx = 3 * n + 1;
  pw = vector<int>(mx);
  pw[0] = 1;
  for (int j = (1); j <= (mx - 1); ++j) pw[j] = (pw[j - 1] * S) % P;
  for (int j = 0; j < (n + 1); ++j)
    for (int i = (j); i >= (0); --i) {
      T[i][j] = vector<int>(mx);
      for (int k = 0; k < (mx); ++k) {
        if (j == i)
          T[i][j][k] = pw[k];
        else if (j == i + 1) {
          if (k > 0) T[i][j][k] = (T[i][j][k - 1] * (S - 1) + pw[k - 1]) % P;
        } else if (j == i + 2 && s[i] == s[j - 1] && k == 1 && odd)
          T[i][j][k] = 0;
        else if (k > 0) {
          if (s[i] == s[j - 1])
            T[i][j][k] =
                (T[i][j][k - 1] * (S - 1) + T[i + 1][j - 1][k - 1]) % P;
          else
            T[i][j][k] = (T[i][j][k - 1] * (S - 2) + T[i + 1][j][k - 1] +
                          T[i][j - 1][k - 1]) %
                         P;
        }
      }
    }
  if (L < n) {
    cout << T[0][n][L] << endl;
    return 0;
  }
  vector<int> coef = solve(T[0][n], n);
  int M = 2 * n + 1;
  vector<int> val(M);
  for (int i = 0; i < (3); ++i) val[i] = pot(S - i, L);
  for (int i = (3); i <= (M - 1); ++i) val[i] = ((long long)val[i - 2] * L) % P;
  long long res = 0;
  for (int i = 0; i < (M); ++i) res = (res + coef[i] * val[i]) % P;
  cout << res << endl;
  return 0;
}
