B. Raintime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are the owner of a harvesting field which can be modeled as an infinite line, whose positions are identified by integers.It will rain for the next n days. On the i-th day, the rain will be centered at position x_i and it will have intensity p_i. Due to these rains, some rainfall will accumulate; let a_j be the amount of rainfall accumulated at integer position j. Initially a_j is 0, and it will increase by \max(0,p_i-|x_i-j|) after the i-th day's rain.A flood will hit your field if, at any moment, there is a position j with accumulated rainfall a_j>m.You can use a magical spell to erase exactly one day's rain, i.e., setting p_i=0. For each i from 1 to n, check whether in case of erasing the i-th day's rain there is no flood.InputEach test contains multiple test cases. The first line contains the number of test cases t (1 \leq t \leq 10^4). The description of the test cases follows.The first line of each test case contains two integers n and m (1 \leq n \leq 2 \cdot 10^5, 1 \leq m \leq 10^9) — the number of rainy days and the maximal accumulated rainfall with no flood occurring.Then n lines follow. The i-th of these lines contains two integers x_i and p_i (1 \leq x_i,p_i \leq 10^9) — the position and intensity of the i-th day's rain.The sum of n over all test cases does not exceed 2 \cdot 10^5.OutputFor each test case, output a binary string s length of n. The i-th character of s is 1 if after erasing the i-th day's rain there is no flood, while it is 0, if after erasing the i-th day's rain the flood still happens.ExampleInput
43 61 55 53 42 31 35 22 51 610 66 124 51 612 55 59 78 3Output
001
11
00
100110
NoteIn the first test case, if we do not use the spell, the accumulated rainfall distribution will be like this:  If we erase the third day's rain, the flood is avoided and the accumulated rainfall distribution looks like this:  In the second test case, since initially the flood will not happen, we can erase any day's rain.In the third test case, there is no way to avoid the flood.
43 61 55 53 42 31 35 22 51 610 66 124 51 612 55 59 78 3
001 11 00 100110 
['binary search', 'brute force', 'data structures', 'geometry', 'greedy', 'implementation', 'math', '*2100']