Problem Description

Bash game: There is a pile of $n$ items. Two players take turns taking items from it. Each time, at least $1$ item and at most $m$ items must be taken; skipping is not allowed. The player who takes the last item wins.

We add some rules to this game:

There is a pile of $n$ items. Player A and player B take turns taking items, and player A goes first. Each time, at least $1$ item and at most $m$ items must be taken. The player who takes all remaining items wins.
Now a new rule is added: you may also choose to take nothing. However, whenever a player chooses to take nothing, in the next $k$ moves, neither player is allowed to take nothing.

For example, when $k=3$, if player A takes nothing in some move, then in the next three turns (player B, player A, player B), they must each take at least $1$ item. After that, it is player A's turn again, and now player A may choose to take nothing again.

Player A and player B play a total of $t$ games. For each game, you need to tell player A whether he has a winning strategy.

Input Format

The first line contains two positive integers $t, op$. When $op=1$, the newly added rule is canceled, but you still need to read $k$ normally.

The next $t$ lines each contain three positive integers $n, m, k$.

Output Format

For each game, if player A has a winning strategy, output Yes. Otherwise output No.

6 0
2 2 2
3 2 2
4 2 2
7 2 3
13 2 6
14 2 6

Yes
Yes
No
Yes
Yes
No

6 0
4 3 2
5 3 3
13 3 5
13 3 6
5 100 1000000000000
123454204 4321 97

Yes
No
Yes
No
Yes
No

Hint

Special property $A$: all $m$ are equal.

For all data: $t \le 10^5$, $1 \le n, m, k \le 10^{18}$.

The testdata is not guaranteed to be random.

Translated by ChatGPT 5