Game with Multiset
Description
In this problem, you are initially given an empty multiset. You have to process two types of queries:
- ADD $x$ — add an element equal to $2^{x}$ to the multiset;
- GET $w$ — say whether it is possible to take the sum of some subset of the current multiset and get a value equal to $w$.
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 $v_i$ ($0 \le v_i \le 10^9$).
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.
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.
5
1 0
1 0
1 0
2 3
2 4
7
1 0
1 1
1 2
1 10
2 4
2 6
2 7
YES
NO
YES
YES
YES