Problem: While most students still sit their exams, the tractor college has completed the summer exam session. In fact, students study only one subject at this college — the Art of Operating a Tractor. Therefore, at the end of a term a student gets only one mark, a three (satisfactory), a four (good) or a five (excellent). Those who score lower marks are unfortunately expelled.

The college has n students, and oddly enough, each of them can be on scholarship. The size of the scholarships varies each term. Since the end-of-the-term exam has just ended, it's time to determine the size of the scholarship to the end of next term.

The monthly budget for the scholarships of the Tractor college is s rubles. To distribute the budget optimally, you must follow these rules:

  * The students who received the same mark for the exam, should receive the same scholarship;
  * Let us denote the size of the scholarship (in roubles) for students who have received marks 3, 4 and 5 for the exam, as k3, k4 and k5, respectively. The values k3, k4 and k5 must be integers and satisfy the inequalities 0 ≤ k3 ≤ k4 ≤ k5;
  * Let's assume that c3, c4, c5 show how many students received marks 3, 4 and 5 for the exam, respectively. The budget of the scholarship should be fully spent on them, that is, c3·k3 + c4·k4 + c5·k5 = s;
  * Let's introduce function <image> — the value that shows how well the scholarships are distributed between students. In the optimal distribution function f(k3, k4, k5) takes the minimum possible value. 



Given the results of the exam, and the budget size s, you have to find the optimal distribution of the scholarship.

Input

The first line has two integers n, s (3 ≤ n ≤ 300, 1 ≤ s ≤ 3·105) — the number of students and the budget size for the scholarship, respectively. The second line contains n integers, where the i-th number represents the mark that the i-th student got for the exam. It is guaranteed that at each mark was given to at least one student.

Output

On a single line print three integers k3, k4 and k5 — the sought values that represent the optimal distribution of the scholarships. If there are multiple optimal answers, print any of them. If there is no answer, print -1.

Examples

Input

5 11
3 4 3 5 5


Output

1 3 3


Input

6 15
5 3 3 4 4 5


Output

-1

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
int n;
int64_t s, a, b, c;
int64_t minVal, x, y, z;
inline int64_t gcd(int64_t x_, int64_t y_, int64_t& t_, int64_t& u_) {
  if (y_ == 0) {
    t_ = 1;
    u_ = 0;
    return x_;
  }
  int64_t res = gcd(y_, x_ % y_, t_, u_);
  int64_t c_ = t_;
  t_ = u_;
  u_ = c_ - u_ * (x_ / y_);
  return res;
}
inline bool solve(int64_t a_, int64_t b_, int64_t c_, int64_t& x_, int64_t& y_,
                  int64_t& g_) {
  g_ = gcd(a_, b_, x_, y_);
  if (c_ % g_) return 0;
  x_ *= (c_ / g_), y_ *= (c_ / g_);
  return 1;
}
inline void check(int64_t xnew, int64_t ynew, int64_t znew) {
  if (a * xnew + b * ynew + c * znew == s && xnew >= 0 && ynew >= xnew &&
      znew >= ynew) {
    if (minVal > abs(a * xnew - b * ynew) + abs(b * ynew - c * znew))
      minVal = abs(a * xnew - b * ynew) + abs(b * ynew - c * znew), x = xnew,
      y = ynew, z = znew;
  } else {
  }
}
int64_t kmin, kmax;
inline int64_t ceildiv(int64_t a, int64_t b) {
  if (a % b) {
    if (a > 0)
      return (a + b) / b;
    else
      return a / b;
  }
  return a / b;
}
inline int64_t floordiv(int64_t a, int64_t b) {
  if (a % b) {
    if (a > 0)
      return a / b;
    else
      return (a - b) / b;
  }
  return a / b;
}
inline void updateXForMin(int64_t val, int64_t x, int64_t cg) {
  kmin = max(kmin, ceildiv(val - x, cg));
}
inline void updateXForMax(int64_t val, int64_t x, int64_t cg) {
  kmax = min(kmax, floordiv(val - x, cg));
}
inline void updateZForMin(int64_t val, int64_t x, int64_t ag) {
  kmin = max(kmin, ceildiv(val - x, ag));
}
inline void updateZForMax(int64_t val, int64_t x, int64_t ag) {
  kmax = min(kmax, floordiv(val - x, ag));
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> s;
  a = 0, b = 0, c = 0;
  char type;
  for (int i = 0; i < n; ++i) {
    cin >> type;
    if (type == '3')
      ++a;
    else if (type == '4')
      ++b;
    else
      ++c;
  }
  minVal = 1e15;
  int64_t xr, zr, g;
  for (int64_t ys = 0; ys < s; ++ys) {
    if (!solve(a, c, s - b * ys, xr, zr, g)) continue;
    kmin = -1e15, kmax = 1e15;
    updateXForMin(ceildiv(b * ys, a), xr, c / g);
    updateXForMin(0, xr, c / g);
    updateXForMax(y, xr, c / g);
    updateZForMin(y, zr, a / g);
    updateZForMax(floordiv(b * y, c), zr, a / g);
    check(xr + kmin * c / g, ys, zr - kmin * a / g),
        check(xr + kmax * c / g, ys, zr - kmax * a / g);
    kmin = -1e15, kmax = 1e15;
    updateXForMin(ceildiv(b * ys, a), xr, c / g);
    updateXForMin(0, xr, c / g);
    updateXForMax(y, xr, c / g);
    updateZForMin(y, zr, a / g);
    updateZForMin(ceildiv(b * y, c), zr, a / g);
    check(xr + kmin * c / g, ys, zr - kmin * a / g),
        check(xr + kmax * c / g, ys, zr - kmax * a / g);
    kmin = -1e15, kmax = 1e15;
    updateXForMax(floordiv(b * ys, a), xr, c / g);
    updateXForMin(0, xr, c / g);
    updateXForMax(y, xr, c / g);
    updateZForMin(y, zr, a / g);
    updateZForMax(floordiv(b * y, c), zr, a / g);
    check(xr + kmin * c / g, ys, zr - kmin * a / g),
        check(xr + kmax * c / g, ys, zr - kmax * a / g);
    kmin = -1e15, kmax = 1e15;
    updateXForMax(floordiv(b * ys, a), xr, c / g);
    updateXForMin(0, xr, c / g);
    updateXForMax(y, xr, c / g);
    updateZForMin(y, zr, a / g);
    updateZForMin(ceildiv(b * y, c), zr, a / g);
    check(xr + kmin * c / g, ys, zr - kmin * a / g),
        check(xr + kmax * c / g, ys, zr - kmax * a / g);
  }
  int64_t oldx = x, oldy = y, oldz = z;
  for (int dx = -350; dx <= 350; ++dx) {
    for (int dy = -350; dy <= 350; ++dy) {
      for (int dz = -350; dz <= 350; ++dz) {
        check(oldx + dx, oldy + dy, oldz + dz);
      }
    }
  }
  if (minVal == int64_t(1e15))
    cout << "-1\n";
  else
    cout << x << " " << y << " " << z << "\n";
  return 0;
}