Speed Limits

Peter is driving to the finals of a programming contest. The main part of his route runs along a newly built highway. He gets on the highway at kilometer $s$ and gets off at kilometer $k$ (with $s < k$). His car has a top speed of $v_{\max}$ kilometers per hour and can change speed instantly.

Peter loves to drive fast. If he covers $x$ kilometers at speed $v$, his satisfaction increases by $x \cdot v$. He wants to drive from kilometer $s$ to kilometer $k$ so that his total satisfaction is as large as possible.

There are $n$ speed limits on the highway. The $i$-th limit applies from kilometer $a_i$ to kilometer $b_i$; inside that range he may not drive faster than $v_i$ kilometers per hour. Where several limits cover the same stretch of road, he must obey all of them at once (that is, the strictest one).

Peter's friends will quietly remove exactly one of the speed limits before he arrives. Peter wants to choose which limit to remove so that his best achievable satisfaction becomes as large as it can be. Determine which limit that is.

The first line contains four integers $n$, $s$, $k$, and $v_{\max}$ separated by single spaces, where $1 \le n \le 100000$, $0 \le s < k \le 1000000$, and $1 \le v_{\max} \le 300$.

Each of the next $n$ lines describes one speed limit. The $(i+1)$-th line contains three integers $a_i$, $b_i$, and $v_i$ separated by single spaces, where $0 \le a_i < b_i \le 1000000$ and $1 \le v_i \le 400$. They mean that from kilometer $a_i$ to kilometer $b_i$ the speed may not exceed $v_i$ kilometers per hour.

Print one integer: the number of the speed limit that should be removed so that Peter's satisfaction is maximized. The speed limits are numbered from $1$ to $n$ in the order they appear in the input. If removing any one of several limits yields the same maximum satisfaction, print the smallest such number.