#include <bits/stdc++.h>
using namespace std;
template <typename T, typename U>
inline void smin(T &a, const U &b) {
  if (a > b) a = b;
}
template <typename T, typename U>
inline void smax(T &a, const U &b) {
  if (a < b) a = b;
}
template <class T>
inline void gn(T &first) {
  char c, sg = 0;
  while (c = getchar(), (c > '9' || c < '0') && c != '-')
    ;
  for ((c == '-' ? sg = 1, c = getchar() : 0), first = 0; c >= '0' && c <= '9';
       c = getchar())
    first = (first << 1) + (first << 3) + c - '0';
  if (sg) first = -first;
}
template <class T1, class T2>
inline void gn(T1 &x1, T2 &x2) {
  gn(x1), gn(x2);
}
template <class T1, class T2, class T3>
inline void gn(T1 &x1, T2 &x2, T3 &x3) {
  gn(x1, x2), gn(x3);
}
template <class T>
inline void print(T first) {
  if (first < 0) {
    putchar('-');
    return print(-first);
  }
  if (first < 10) {
    putchar('0' + first);
    return;
  }
  print(first / 10);
  putchar(first % 10 + '0');
}
template <class T>
inline void println(T first) {
  print(first);
  putchar('\n');
}
template <class T>
inline void printsp(T first) {
  print(first);
  putchar(' ');
}
template <class T1, class T2>
inline void print(T1 x1, T2 x2) {
  printsp(x1), println(x2);
}
template <class T1, class T2, class T3>
inline void print(T1 x1, T2 x2, T3 x3) {
  printsp(x1), printsp(x2), println(x3);
}
int power(int a, int b, int m, int ans = 1) {
  for (; b; b >>= 1, a = (long long)a * a % m)
    if (b & 1) ans = (long long)ans * a % m;
  return ans;
}
map<double, int> num;
vector<double> s;
int main() {
  int n;
  double d;
  scanf("%d %lf", &n, &d);
  while (n--) {
    double first, second, r;
    scanf("%lf %lf %lf", &first, &second, &r);
    double D2 = first * first + second * second, D = sqrt(D2);
    double len = (int)((D - r) / d) * d;
    if (len < D - r - 1e-8) len += d;
    double kong = atan2(second, first) + 100;
    for (; len < D + r + 1e-8; len += d) {
      double al = acos((D2 + len * len - r * r) / 2 / D / len);
      double st = kong - al, ed = kong + al + 1e-8;
      num[st]++;
      num[ed]--;
      s.push_back(st), s.push_back(ed);
    }
  }
  sort(s.begin(), s.end());
  s.resize(unique(s.begin(), s.end()) - s.begin());
  int ans = 0;
  double prv = 1999.0728;
  for (int i = 0; i < s.size(); i++) {
    num[s[i]] += num[prv];
    smax(ans, num[s[i]]);
    prv = s[i];
  }
  println(ans);
}
