A 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*<sub class="lower-index">*i*</sub> of water in the vessels and the desired amounts *b*<sub class="lower-index">*i*</sub> find a sequence of transfusions that deals with the task. Total number of transfusions must not exceed 2·*n*<sup class="upper-index">2</sup>.
First line of the input contains integers *n*, *v*, *e* (1 ≤ *n* ≤ 300, 1 ≤ *v* ≤ 10<sup class="upper-index">9</sup>, 0 ≤ *e* ≤ 50000).

Next two lines contain *n* integers each: initial *a*<sub class="lower-index">*i*</sub> and the desired amounts *b*<sub class="lower-index">*i*</sub> of water in corresponding vessels (0 ≤ *a*<sub class="lower-index">*i*</sub>, *b*<sub class="lower-index">*i*</sub> ≤ *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.
print("_RANDOM_GUESS_1689347967.4548218")# 1689347967.454852