/* -*- coding: utf-8 -*-
 *
 * 2389.cc:  No.2389 Cheating Code Golf - yukicoder
 */

#include<cstdio>
#include<algorithm>
 
using namespace std;

/* constant */

const int MAX_N = 12;
const int NBITS = 1 << MAX_N;
const int MAX_M = 40;

/* typedef */

/* global variables */

int as[MAX_N], bs[MAX_N], ps[MAX_N];
double invas[MAX_N], invbs[MAX_N], invps[MAX_N];
double dp[NBITS][MAX_M + 1];

/* subroutines */

inline void setmax(double &a, double b) { if (a < b) a = b; }

/* main */

int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  for (int i = 0; i < n; i++) scanf("%d%d%d", as + i, bs + i, ps + i);

  for (int i = 0; i < n; i++) {
    invas[i] = 1.0 / as[i], invbs[i] = 1.0 / bs[i];
    invps[i] = 1.0 / ps[i];
  }

  int nbits = 1 << n;

  for (int bits = 0; bits < nbits; bits++)
    for (int i = 0; i <= m; i++) {
      for (int j = 0, bj = 1; j < n; j++, bj <<= 1)
	if (bits & bj) {
	  setmax(dp[bits][i], dp[bits ^ bj][i] + invas[j]);
	  if (i > 0)
	    setmax(dp[bits][i],
		   (dp[bits ^ bj][i] + invbs[j]) * invps[j] +
		   dp[bits][i - 1] * (1.0 - invps[j]));
	}
    }

  printf("%.12lf\n", dp[nbits - 1][m]);
  
  return 0;
}