CF1070M Algoland and Berland

Once upon a time Algoland and Berland were a single country, but those times are long gone. Now they are two different countries, but their cities are scattered on a common territory. All cities are represented as points on the Cartesian plane. Algoland consists of $ a $ cities numbered from $ 1 $ to $ a $ . The coordinates of the $ i $ -th Algoland city are a pair of integer numbers $ (xa_i, ya_i) $ . Similarly, Berland consists of $ b $ cities numbered from $ 1 $ to $ b $ . The coordinates of the $ j $ -th Berland city are a pair of integer numbers $ (xb_j, yb_j) $ . No three of the $ a+b $ mentioned cities lie on a single straight line. As the first step to unite the countries, Berland decided to build several bidirectional freeways. Each freeway is going to be a line segment that starts in a Berland city and ends in an Algoland city. Freeways can't intersect with each other at any point except freeway's start or end. Moreover, the freeways have to connect all $ a+b $ cities. Here, connectivity means that one can get from any of the specified $ a+b $ cities to any other of the $ a+b $ cities using freeways. Note that all freeways are bidirectional, which means that one can drive on each of them in both directions. Mayor of each of the $ b $ Berland cities allocated a budget to build the freeways that start from this city. Thus, you are given the numbers $ r_1, r_2, \dots, r_b $ , where $ r_j $ is the number of freeways that are going to start in the $ j $ -th Berland city. The total allocated budget is very tight and only covers building the minimal necessary set of freeways. In other words, $ r_1+r_2+\dots+r_b=a+b-1 $ . Help Berland to build the freeways so that: - each freeway is a line segment connecting a Berland city and an Algoland city, - no freeways intersect with each other except for the freeway's start or end, - freeways connect all $ a+b $ cities (all freeways are bidirectional), - there are $ r_j $ freeways that start from the $ j $ -th Berland city.

Input contains one or several test cases. The first input line contains a single integer number $ t $ ( $ 1 \le t \le 3000 $ ) — number of test cases. Then, $ t $ test cases follow. Solve test cases separately, test cases are completely independent and do not affect each other. Each test case starts with a line containing space-separated integers $ a $ and $ b $ ( $ 1 \le a, b \le 3000 $ ) — numbers of Algoland cities and number of Berland cities correspondingly. The next line contains $ b $ space-separated integers $ r_1, r_2, \dots, r_b $ ( $ 1 \le r_b \le a $ ) where $ r_j $ is the number of freeways, that should start in the $ j $ -th Berland city. It is guaranteed that $ r_1+r_2+\dots+r_b=a+b-1 $ . The next $ a $ lines contain coordinates of the Algoland cities — pairs of space-separated integers $ xa_i, ya_i $ ( $ -10000 \le xa_i, ya_i \le 10000 $ ). The next $ b $ lines contain coordinates of the Berland cities — pairs of space-separated integers $ xb_i, yb_i $ ( $ -10000 \le xb_i, yb_i \le 10000 $ ). All cities are located at distinct points, no three of the $ a+b $ cities lie on a single straight line. Sum of values $ a $ across all test cases doesn't exceed $ 3000 $ . Sum of values $ b $ across all test cases doesn't exceed $ 3000 $ .

For each of the $ t $ test cases, first print "YES" if there is an answer or "NO" otherwise. If there is an answer, print the freeway building plan in the next $ a+b-1 $ lines. Each line of the plan should contain two space-separated integers $ j $ and $ i $ which means that a freeway from the $ j $ -th Berland city to the $ i $ -th Algoland city should be built. If there are multiple solutions, print any.