#include <bits/stdc++.h>

using namespace std;

int P;

template <typename T>
T power(T a, long long b) {
  T r = 1;
  while (b) {
    if (b & 1) {
      r *= a;
    }
    a *= a;
    b >>= 1;
  }
  return r;
}

int inverse(int a, int m) {
  a %= m;
  if (a < 0) {
    a += m;
  }
  int b = m, u = 0, v = 1;
  while (a) {
    int t = b / a;
    b -= a * t;
    swap(a, b);
    u -= v * t;
    swap(u, v);
  }
  if (u < 0) {
    u += m;
  }
  return u;
}

struct modnum {
 private:
  int v;

 public:
  modnum() : v(0) {
  }

  modnum(long long _v) {
    v = _v % P;
    if (v < 0) {
      v += P;
    }
  }

  explicit operator int() const {
    return v;
  }

  bool operator==(const modnum& o) const {
    return v == o.v;
  }

  bool operator!=(const modnum& o) const {
    return v != o.v;
  }

  modnum inverse() const {
    return modnum(::inverse(v, P));
  }

  modnum operator-() const {
    return modnum(v ? P - v : 0);
  }
  
  modnum operator+() const {
    return *this;
  }

  modnum& operator++() {
    v++;
    if (v == P) {
      v = 0;
    }
    return *this;
  }
  
  modnum& operator--() {
    if (v == 0) {
      v = P;
    }
    v--;
    return *this;
  }

  modnum operator++(int) {
    modnum r = *this;
    ++*this;
    return r;
  }
  
  modnum operator--(int) {
    modnum r = *this;
    --*this;
    return r;
  }

  modnum& operator+=(const modnum& o) {
    v += o.v;
    if (v >= P) {
      v -= P;
    }
    return *this;
  }

  modnum operator+(const modnum& o) const {
    return modnum(*this) += o;
  }

  modnum& operator-=(const modnum& o) {
    v -= o.v;
    if (v < 0) {
      v += P;
    }
    return *this;
  }

  modnum operator-(const modnum& o) const {
    return modnum(*this) -= o;
  }

  modnum& operator*=(const modnum& o) {
    v = (int) ((long long) v * o.v % P);
    return *this;
  }

  modnum operator*(const modnum& o) const {
    return modnum(*this) *= o;
  }
  
  modnum& operator/=(const modnum& o) {
    return *this *= o.inverse();
  }

  modnum operator/(const modnum& o) const {
    return modnum(*this) /= o;
  }
};

ostream& operator<<(ostream& out, const modnum& n) {
  return out << int(n);
}

istream& operator>>(istream& in, modnum& n) {
  long long _v;
  in >> _v;
  n = modnum(_v);
  return in;
}

using num = modnum;

int main() {
#ifdef LOCAL
  freopen("input.txt", "r", stdin);
#endif
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n >> P;
  vector<pair<int, int>> ord;
  for (int i = 0; i < n; ++i) {
    ord.emplace_back(sqrt(n * n - i * i - 1) + 1, min(n * 2, (int) sqrt(4 * n * n - i * i) + 1));
  }
  for (int i = n; i < n * 2; ++i) {
    ord.emplace_back(sqrt(4 * n * n - i * i) + 1, -1);
  }
  sort(ord.begin(), ord.end());
  num ans = 0;
  for (int d = 0; d <= n; ++d) {
    vector<num> dp(d + 1);
    dp[0] = 1;
    int u = 0;
    int v = 0;
    for (auto p : ord) {
      if (p.second != -1) {
        for (int i = d; ~i; --i) {
          if (i < d) {
            dp[i + 1] += dp[i] * (p.first - i - v);
          }
          dp[i] *= p.second - n - d - u + i;
        }
        ++u;
      } else {
        for (int i = d; ~i; --i) {
          dp[i] *= p.first - i - v;
        }
        ++v;
      }
    }
    ans += dp[d] * (1 - (d & 1) * 2);
  }
  cout << ans << "\n";
  return 0;
}


Measured memory_bytes: 256