F. Trucks and Citiestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere 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.InputFirst line contains two integers n and m (2 \le n \le 400, 1 \le m \le 250000) — the number of cities and trucks.The second line contains n integers a_1, a_2, \dots, a_n (1 \le a_i \le 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 \le s_i < f_i \le n, 1 \le c_i \le 10^9, 0 \le r_i \le n) — the description of the i-th truck.OutputPrint the only integer — minimum possible size of gas-tanks V such that all trucks can reach their destinations.ExampleInput
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
NoteLet's look at queries in details:   the 1-st truck must arrive at position 7 from 2 without refuelling, so it needs gas-tank of volume at least 50.  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.  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.  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.  the 5-th truck has the same description, so it also needs gas-tank of volume at least 40.  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. 
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

55 
['binary search', 'dp', '*2400']