write a go solution for Description:
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.

Input Format:
Each test contains multiple test cases. The first line contains the number of test cases t (1<=t<=10^4). The description of the test cases follows.

The first line of each test case contains two integers n and m (1<=n<=2*10^5, 1<=m<=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<=x_i,p_i<=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*10^5.

Output Format:
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.

Note:
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:

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.. Output only the code with no comments, explanation, or additional text.