Have you ever heard of the 3SUM problem? Yoodam, who has researched the 3SUM problem all his life, has developed an excellent $O(\frac{N\sqrt{N}\log^2 N}{64})$ algorithm that solves the following variation of the 3SUM problem.

• For a sequence $\{A_1, A_2, \cdots, A_N\}$ of length $N$ and a positive integer $M$, do three numbers $i, j, k$ such that $A_i+A_j+A_k\equiv 0 \pmod M$ and $1\le i<j<k\le N$ exist?

Yoodam wants to propose this amazing discovery as a problem to share it with many people. However, having spent too much energy developing the algorithm, he generated the data only in the following way.

• Choose two numbers $N$ and $M$ in the range $3\le N\le 300\,000$ and $1\le M\le 10^{18}$.
• Set the sequence $A$ to $\{1\mod M, 2\mod M, \cdots, 2^{N-1} \mod M\}$.

You want to take advantage of this weak data to solve the problem without using Yoodam's algorithm! Given the sequence generated in the above manner and $M$, determine whether there exist three integers $i, j, k$ such that $A_i+A_j+A_k\equiv 0 \pmod M$ and $1\le i<j<k\le N$, and if they exist, find such three integers.

The input is given in the following format.

$N\ M$ $A_1\ A_2\ \cdots \ A_N$

If there exist three integers $i, j, k$ satisfying the problem's conditions, print as follows.

$\rm{YES}$ $i\ j\ k$

If such $i, j, k$ do not exist, print as follows.

$\rm{NO}$

• $3\le N\le 300\,000$.
• $1\le M\le 10^{18}$.