Sum Sequence

Futsal fiend Dongwoo always gathers people around him to play futsal. Among the futsal members Dongwoo gathered were Jaewoo, Jongwoo, Hyunchul, Junhyeok, Yongmyeong, Jaehyun, Donghyun, Geunhyeong, Dohun, Minseong, Munseong, Sejun, and many others. Many of them were recruited last year, at the Ilsan futsal gathering held after the 2024 ICPC Seoul Regional, as problem setters or testers for <6th MatKor Cup:2025 Winter>.

Jaewoo received a sequence from Dohun and wants to give back a sum sequence rather than a sequence of sums. Jaewoo builds the sum sequence with the following process.

At first, the set $A=\mathbb{Z}^+$ contains all positive integers. Repeat the following process $10^{1\,000\,000}$ times on this set to build a new sequence $B_M$.

1. Choose the $M$ smallest numbers in $A$, and compute their sum $S$.
2. For each of the $M$ chosen numbers, if that number is in $A$, remove it from $A$. Also, if $S$ is in $A$, remove $S$ from $A$.
3. Append $S$ to $B_M$.

For example, when $M=3$, $1+2+3=6$, $4+5+7=16$, $8+9+10=27$, $11+12+13=36$, and $14+15+17=46$, so $B_3=[6, 16, 27, 36, 46, 57, 66, 75, \cdots]$.

Given $M$ and $Q$ queries, determine for each query whether that number is in $B_M$.

The first line contains $M(1\le M\le 10^{18})$ and $Q(1\le Q\le 10^5)$, separated by a space. Each of the next $Q$ lines contains one integer $N(1\le N\le 10^{18})$, the number to check.

For each query, print 1 if the number is in $B_M$, otherwise print 0, one per line.