Problem: There are n cities along the road, which can be represented as a straight line. The i-th city is situated at the distance of a_i kilometers from the origin. All cities are situated in the same direction from the origin. There are m trucks travelling from one city to another. 

Each truck can be described by 4 integers: starting city s_i, finishing city f_i, fuel consumption c_i and number of possible refuelings r_i. The i-th truck will spend c_i litres of fuel per one kilometer. 

When a truck arrives in some city, it can be refueled (but refueling is impossible in the middle of nowhere). The i-th truck can be refueled at most r_i times. Each refueling makes truck's gas-tank full. All trucks start with full gas-tank.

All trucks will have gas-tanks of the same size V litres. You should find minimum possible V such that all trucks can reach their destinations without refueling more times than allowed.

Input

First line contains two integers n and m (2 ≤ n ≤ 400, 1 ≤ m ≤ 250000) — the number of cities and trucks.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9, a_i < a_{i+1}) — positions of cities in the ascending order.

Next m lines contains 4 integers each. The i-th line contains integers s_i, f_i, c_i, r_i (1 ≤ s_i < f_i ≤ n, 1 ≤ c_i ≤ 10^9, 0 ≤ r_i ≤ n) — the description of the i-th truck.

Output

Print the only integer — minimum possible size of gas-tanks V such that all trucks can reach their destinations.

Example

Input


7 6
2 5 7 10 14 15 17
1 3 10 0
1 7 12 7
4 5 13 3
4 7 10 1
4 7 10 1
1 5 11 2


Output


55

Note

Let's look at queries in details: 

  1. the 1-st truck must arrive at position 7 from 2 without refuelling, so it needs gas-tank of volume at least 50. 
  2. the 2-nd truck must arrive at position 17 from 2 and can be refueled at any city (if it is on the path between starting point and ending point), so it needs gas-tank of volume at least 48. 
  3. the 3-rd truck must arrive at position 14 from 10, there is no city between, so it needs gas-tank of volume at least 52. 
  4. the 4-th truck must arrive at position 17 from 10 and can be refueled only one time: it's optimal to refuel at 5-th city (position 14) so it needs gas-tank of volume at least 40. 
  5. the 5-th truck has the same description, so it also needs gas-tank of volume at least 40. 
  6. the 6-th truck must arrive at position 14 from 2 and can be refueled two times: first time in city 2 or 3 and second time in city 4 so it needs gas-tank of volume at least 55. 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long n, m, d[410], ans;
long long s[250000], e[250000], c[250000], re[250000];
long long id[250000];
bool check(long long id, long long V) {
  long long start = s[id], end = e[id], cost = c[id], now = V, i, cnt = 0;
  for (i = start + 1; i <= end; i++) {
    if (V < cost * (d[i] - d[i - 1])) return 0;
    if (now < cost * (d[i] - d[i - 1])) {
      now = V;
      cnt++;
    }
    now -= cost * (d[i] - d[i - 1]);
  }
  return cnt <= re[id];
}
int main() {
  long long i, l, r, mid;
  srand(time(0));
  scanf("%d%d", &n, &m);
  for (i = 1; i <= n; i++) scanf("%d", &d[i]);
  for (i = 0; i < m; i++) {
    scanf("%d%d%d%d", &s[i], &e[i], &c[i], &re[i]);
    id[i] = i;
  }
  random_shuffle(id, id + m);
  for (i = 0; i < m; i++)
    if (!check(id[i], ans)) {
      l = ans;
      r = 4557430888798830399LL;
      while (l + 1 < r) {
        mid = (l + r) >> 1LL;
        if (check(id[i], mid))
          r = mid;
        else
          l = mid;
      }
      ans = max(ans, r);
    }
  printf("%lld", ans);
}