There is an array of length $N$. Two players, A and B, play a game on this array. Initially, some cells are white and some are black. The two players take turns making moves. In each move, a player chooses a white cell at index $x$. Then, they choose an integer $k$ such that $1 \le k \le N/x$, and flip the colors of the cells at indices $x, 2x, \dots, kx$. The player who cannot make a move loses.

Player A (the first player) has several queries. For each query, you are given the initial state of the array, and you must determine if the first player has a winning strategy.

Input

The first line contains an integer $N$, representing the length of the array. The second line contains an integer $K$, representing the number of queries. The next $2 \times K$ lines describe the queries. Each query consists of two lines: the first line contains a positive integer $W$, representing the number of white cells in the array, and the second line contains $W$ positive integers between $1$ and $N$, representing the indices of the white cells.

Output

For each query, output "Yes" if the first player has a winning strategy, otherwise output "No". Separate the answers with newlines.

Examples

Input 1

3
2
2
1 2
2
2 3

Output 1

Yes
No

Note

In the first query, player A chooses index $1$, then flips the cells at $1 \times 1$ and $2 \times 1$. In the second query, no matter which cell player A chooses, they can only flip one cell. Player B only needs to flip the other cell to win.

Constraints

For $30\%$ of the data, $N \le 20$. For $50\%$ of the data, $N \le 1\,000\,000$. For $70\%$ of the data, $N \le 10\,000\,000$. For $100\%$ of the data, $N \le 1\,000\,000\,000$, $K, W \le 100$, and no cell will appear multiple times in the same query.