B"You 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. Each test contains multiple test cases. The first line contains the number of test cases t ( 1 <= q t <= q 10^4 ). The description of the test cases follows. The first line of each test case contains two integers n and m ( 1 <= q n <= q 2 cdot 10^5 , 1 <= q m <= q 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 <= q x_i,p_i <= q 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 . For 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. In 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: "...