#include <bits/stdc++.h>
using namespace std;
template <typename T>
void maxtt(T& t1, T t2) {
  t1 = max(t1, t2);
}
template <typename T>
void mintt(T& t1, T t2) {
  t1 = min(t1, t2);
}
bool debug = 0;
int n, m, k;
int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0};
string direc = "RDLU";
long long ln, lk, lm;
void etp(bool f = 0) {
  puts(f ? "YES" : "NO");
  exit(0);
}
void addmod(int& x, int y, int mod = 998244353) {
  assert(y >= 0);
  x += y;
  if (x >= mod) x -= mod;
  assert(x >= 0 && x < mod);
}
void et(int x = -1) {
  printf("%d\n", x);
  exit(0);
}
long long fastPow(long long x, long long y, int mod = 998244353) {
  long long ans = 1;
  while (y > 0) {
    if (y & 1) ans = (x * ans) % mod;
    x = x * x % mod;
    y >>= 1;
  }
  return ans;
}
long long gcd1(long long x, long long y) { return y ? gcd1(y, x % y) : x; }
int t;
long long a[205], b[205], c[205];
long long sa[205], sb[205];
long long f[205][205][2], g[205][205][2];
void fmain(int ID) {
  scanf("%d%d%d", &n, &t, &k);
  for (int(i) = 1; (i) <= (int)(n); (i)++) {
    scanf("%lld%lld%lld", a + i, b + i, c + i);
  }
  n++;
  a[n] = (1 << 30);
  b[n] = (1 << 30);
  c[n] = (1LL << 60);
  for (int(i) = 1; (i) <= (int)(n); (i)++) {
    sa[i] = sa[i - 1] + a[i];
    sb[i] = sb[i - 1] + b[i];
  }
  for (int(i) = 0; (i) < (int)(205); (i)++)
    for (int(j) = 0; (j) < (int)(205); (j)++)
      for (int(z) = 0; (z) < (int)(2); (z)++) {
        f[i][j][z] = g[i][j][z] = (1LL << 60);
      }
  for (int(j) = 0; (j) < (int)(205); (j)++)
    for (int(z) = 0; (z) < (int)(2); (z)++) f[0][j][z] = g[0][j][z] = 0;
  for (int(i) = 1; (i) <= (int)(n); (i)++) {
    for (int j = 0; j <= t; j++)
      for (int(z) = 0; (z) < (int)(2); (z)++) {
        if (a[i] * z + b[i] * j <= c[i] && f[i - 1][j][z] < (1LL << 60)) {
          mintt(f[i][j][z], f[i - 1][j][z]);
          long long cnt = (sa[i - 1] * z + sb[i - 1] * j + k - 1) / k;
          if (cnt * k <= sa[i] * z + sb[i] * j) mintt(g[i][j][z], cnt);
        }
        for (int r = 0; r < j; r++) {
          long long cnt = g[i][r][z];
          if (cnt == (1LL << 60)) continue;
          long long rem = sa[i] * z + sb[i] * r - cnt * k;
          assert(0 <= rem);
          long long need = (max(0LL, rem + b[i] * (j - r) - c[i]) + k - 1) / k;
          if (need * k <= rem && f[i - 1][j - r][0] < (1LL << 60)) {
            mintt(f[i][j][z], cnt + need + f[i - 1][j - r][0]);
            long long n2 = (sb[i - 1] * (j - r) + k - 1) / k;
            if (n2 * k <= sb[i] * (j - r) + rem - need * k) {
              mintt(g[i][j][z], cnt + need + n2);
            }
          }
        }
      }
  }
  printf("%lld\n", f[n][t][1]);
}
int main() {
  int t = 1;
  for (int(i) = 1; (i) <= (int)(t); (i)++) {
    fmain(i);
  }
  return 0;
}
