Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Volleyball

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPetya loves volleyball very much. One day he was running late for a volleyball match. Petya hasn't bought his own car yet, that's why he had to take a taxi. The city has *n* junctions, some of which are connected by two-way roads. The length of each road is defined by some positive integer number of meters; the roads can have different lengths.

Initially each junction has exactly one taxi standing there. The taxi driver from the *i*-th junction agrees to drive Petya (perhaps through several intermediate junctions) to some other junction if the travel distance is not more than *t*_{i} meters. Also, the cost of the ride doesn't depend on the distance and is equal to *c*_{i} bourles. Taxis can't stop in the middle of a road. Each taxi can be used no more than once. Petya can catch taxi only in the junction, where it stands initially.

At the moment Petya is located on the junction *x* and the volleyball stadium is on the junction *y*. Determine the minimum amount of money Petya will need to drive to the stadium.

Input

The first line contains two integers *n* and *m* (1 ≤ *n* ≤ 1000, 0 ≤ *m* ≤ 1000). They are the number of junctions and roads in the city correspondingly. The junctions are numbered from 1 to *n*, inclusive. The next line contains two integers *x* and *y* (1 ≤ *x*, *y* ≤ *n*). They are the numbers of the initial and final junctions correspondingly. Next *m* lines contain the roads' description. Each road is described by a group of three integers *u*_{i}, *v*_{i}, *w*_{i} (1 ≤ *u*_{i}, *v*_{i} ≤ *n*, 1 ≤ *w*_{i} ≤ 10^{9}) — they are the numbers of the junctions connected by the road and the length of the road, correspondingly. The next *n* lines contain *n* pairs of integers *t*_{i} and *c*_{i} (1 ≤ *t*_{i}, *c*_{i} ≤ 10^{9}), which describe the taxi driver that waits at the *i*-th junction — the maximum distance he can drive and the drive's cost. The road can't connect the junction with itself, but between a pair of junctions there can be more than one road. All consecutive numbers in each line are separated by exactly one space character.

Output

If taxis can't drive Petya to the destination point, print "-1" (without the quotes). Otherwise, print the drive's minimum cost.

Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specificator.

Examples

Input

4 4

1 3

1 2 3

1 4 1

2 4 1

2 3 5

2 7

7 2

1 2

7 7

Output

9

Note

An optimal way — ride from the junction 1 to 2 (via junction 4), then from 2 to 3. It costs 7+2=9 bourles.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/24/2019 06:11:37 (e1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|