C. Game with Multiset
time limit per test
1.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

In this problem, you are initially given an empty multiset. You have to process two types of queries:

  1. ADD $$$x$$$ — add an element equal to $$$2^{x}$$$ to the multiset;
  2. GET $$$w$$$ — say whether it is possible to take the sum of some subset of the current multiset and get a value equal to $$$w$$$.
Input

The first line contains one integer $$$m$$$ ($$$1 \le m \le 10^5$$$) — the number of queries.

Then $$$m$$$ lines follow, each of which contains two integers $$$t_i$$$, $$$v_i$$$, denoting the $$$i$$$-th query. If $$$t_i = 1$$$, then the $$$i$$$-th query is ADD $$$v_i$$$ ($$$0 \le v_i \le 29$$$). If $$$t_i = 2$$$, then the $$$i$$$-th query is GET $$$v_i$$$ ($$$0 \le v_i \le 10^9$$$).

Output

For each GET query, print YES if it is possible to choose a subset with sum equal to $$$w$$$, or NO if it is impossible.

Examples
Input
5
1 0
1 0
1 0
2 3
2 4
Output
YES
NO
Input
7
1 0
1 1
1 2
1 10
2 4
2 6
2 7
Output
YES
YES
YES