Problem: Consider a system of n water taps all pouring water into the same container. The i-th water tap can be set to deliver any amount of water from 0 to ai ml per second (this amount may be a real number). The water delivered by i-th tap has temperature ti.

If for every <image> you set i-th tap to deliver exactly xi ml of water per second, then the resulting temperature of water will be <image> (if <image>, then to avoid division by zero we state that the resulting water temperature is 0).

You have to set all the water taps in such a way that the resulting temperature is exactly T. What is the maximum amount of water you may get per second if its temperature has to be T?

Input

The first line contains two integers n and T (1 ≤ n ≤ 200000, 1 ≤ T ≤ 106) — the number of water taps and the desired temperature of water, respectively.

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106) where ai is the maximum amount of water i-th tap can deliver per second.

The third line contains n integers t1, t2, ..., tn (1 ≤ ti ≤ 106) — the temperature of water each tap delivers.

Output

Print the maximum possible amount of water with temperature exactly T you can get per second (if it is impossible to obtain water with such temperature, then the answer is considered to be 0).

Your answer is considered correct if its absolute or relative error doesn't exceed 10 - 6.

Examples

Input

2 100
3 10
50 150


Output

6.000000000000000


Input

3 9
5 5 30
6 6 10


Output

40.000000000000000


Input

2 12
1 3
10 15


Output

1.666666666666667

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
bool db = false;
const long double INF = 1e18 + 1;
const long double EPS = 1e-10;
const long long maxn = 2 * 1e5;
long long N, T;
pair<long double, long double> in[maxn];
long double a[maxn];
long double t[maxn];
long double ans = 0;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> N >> T;
  long double ldT = T;
  ans = 0.0;
  for (int i = 0; i < N; i++) {
    cin >> in[i].second;
  }
  for (int i = 0; i < N; i++) {
    cin >> in[i].first;
    if (in[i].first == T) ans += in[i].second;
  }
  sort(in, in + N);
  vector<pair<long double, long double> > hots;
  vector<pair<long double, long double> > colds;
  for (int i = 0; i < N; i++) {
    if (in[i].first > ldT) {
      auto ta = in[i];
      ta.first = ta.first - ldT;
      hots.push_back(ta);
    } else if (in[i].first < ldT) {
      auto ta = in[i];
      ta.first = ldT - ta.first;
      colds.push_back(ta);
    }
  }
  if (hots.size() == 0 or colds.size() == 0) {
    cout << ans << endl;
    return 0;
  }
  reverse(colds.begin(), colds.end());
  hots.insert(hots.begin(), {0.0, 0.0});
  colds.insert(colds.begin(), {0.0, 0.0});
  vector<long double> cs_a_hots(hots.size(), 0.0);
  vector<long double> cs_a_colds(colds.size(), 0.0);
  vector<long double> cs_e_hots(hots.size(), 0.0);
  vector<long double> cs_e_colds(colds.size(), 0.0);
  for (int i = 0; i < hots.size(); i++) {
    cs_e_hots[i] = hots[i].first * hots[i].second;
    if (i) cs_e_hots[i] += cs_e_hots[i - 1];
    cs_a_hots[i] = hots[i].second;
    if (i) cs_a_hots[i] += cs_a_hots[i - 1];
  }
  for (int i = 0; i < colds.size(); i++) {
    cs_e_colds[i] = colds[i].first * colds[i].second;
    if (i) cs_e_colds[i] += cs_e_colds[i - 1];
    cs_a_colds[i] = colds[i].second;
    if (i) cs_a_colds[i] += cs_a_colds[i - 1];
  }
  long double hot_e_sum_ss = 0.0;
  long double hot_litres_sum = 0.0;
  long double hot_litres_extra = 0.0;
  long double cold_litres_sum = 0.0;
  long double cold_litres_extra = 0.0;
  int cidx = 0;
  int cidx_snapshot = -1;
  int cs_e_colds_sz = cs_e_colds.size();
  long double L;
  long double R;
  long double M;
  long double extra_ans = 0.0;
  for (int i = 1; i < hots.size(); i++) {
    auto [t, a] = hots[i];
    long double tans = 0.0;
    long double hot_e_sum__prefix = cs_e_hots[i - 1];
    long long hot_e_sum__full = cs_e_hots[i];
    int cold_idx =
        lower_bound(cs_e_colds.begin(), cs_e_colds.end(), hot_e_sum__full) -
        cs_e_colds.begin();
    if (cold_idx != cs_e_colds_sz) {
      if (i == hots.size() - 1) {
        hot_litres_sum = cs_a_hots[i];
        hot_litres_extra = 0.0;
        cidx = cold_idx;
        cold_litres_sum = cs_a_colds[cidx - 1];
        cold_litres_extra = 0;
        long double cold_energy_extra =
            (hot_e_sum__full - cs_e_colds[cidx - 1]);
        cold_litres_extra = (cold_energy_extra / colds[cidx].first);
        tans = hot_litres_sum + hot_litres_extra + cold_litres_sum +
               cold_litres_extra;
        extra_ans = max(extra_ans, tans);
        break;
      }
      continue;
    }
    cold_idx =
        lower_bound(cs_e_colds.begin(), cs_e_colds.end(), hot_e_sum__prefix) -
        cs_e_colds.begin();
    assert(cold_idx != cs_e_colds_sz);
    hot_e_sum_ss = hot_e_sum__prefix + 0.0;
    hot_litres_sum = cs_a_hots[i - 1];
    hot_litres_extra = 0.0;
    L = 0.0;
    R = a;
    M;
    while (R - L > EPS) {
      M = (L + R) / 2;
      long double hot_e_sum_with_fraction = hot_e_sum__prefix;
      hot_e_sum_with_fraction += (M * t);
      cidx = lower_bound(cs_e_colds.begin(), cs_e_colds.end(),
                         hot_e_sum_with_fraction) -
             cs_e_colds.begin();
      if (cidx != cs_e_colds_sz) {
        L = M;
        cidx_snapshot = cidx;
        hot_litres_extra = L;
        hot_e_sum_ss = hot_e_sum_with_fraction;
      } else {
        R = M;
      }
    }
    tans = 0.0;
    cidx = cidx_snapshot;
    cold_litres_sum = cs_a_colds[cidx - 1];
    cold_litres_extra = 0;
    long double cold_energy_extra = (hot_e_sum_ss - cs_e_colds[cidx - 1]);
    cold_litres_extra = (cold_energy_extra / colds[cidx].first);
    tans =
        hot_litres_sum + hot_litres_extra + cold_litres_sum + cold_litres_extra;
    extra_ans = max(extra_ans, tans);
    break;
  }
  ans += extra_ans;
  cout << setprecision(12) << ans << endl;
  return 0;
}