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. Balance

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA system of *n* vessels with water is given. Several pairs of vessels are connected by tubes with transfusion mechanisms. One may transfer an integer amount of liters of water between two vessels connected by such tube (tube works in both directions). There might be multiple tubes between two vessels. Total number of tubes equals *e*. Volume of each vessel equals *v* liters. Of course, the amount of the water in any vessel cannot exceed *v* liters in the process of transfusions.

Given the initial amounts *a*_{i} of water in the vessels and the desired amounts *b*_{i} find a sequence of transfusions that deals with the task. Total number of transfusions must not exceed 2·*n*^{2}.

Input

First line of the input contains integers *n*, *v*, *e* (1 ≤ *n* ≤ 300, 1 ≤ *v* ≤ 10^{9}, 0 ≤ *e* ≤ 50000).

Next two lines contain *n* integers each: initial *a*_{i} and the desired amounts *b*_{i} of water in corresponding vessels (0 ≤ *a*_{i}, *b*_{i} ≤ *v*).

Next *e* lines describe one tube each in the format *x* *y* (1 ≤ *x*, *y* ≤ *n*, *x* ≠ *y*) for a tube between vessels number *x* and *y*. There might be multiple tubes between two vessels. You may assume that vessels are numbered from 1 to *n* in some way.

Output

Print "NO" (without quotes), if such sequence of transfusions does not exist.

Otherwise print any suitable sequence in the following format. On the first line print the total number of transfusions *k* (*k* should not exceed 2·*n*^{2}). In the following *k* lines print transfusions in the format *x* *y* *d* (transfusion of *d* liters from the vessel number *x* to the vessel number *y*, *x* and *y* must be distinct). For all transfusions *d* must be a non-negative integer.

Examples

Input

2 10 1

1 9

5 5

1 2

Output

1

2 1 4

Input

2 10 0

5 2

4 2

Output

NO

Input

2 10 0

4 2

4 2

Output

0

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/21/2020 10:49:18 (i1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|