13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T5ac,

You are given an array $$$a_1, a_2, \ldots, a_n$$$ and an integer $$$x$$$.

Find the number of non-empty subsets of indices of this array $$$1 \leq b_1 \lt b_2 \lt \ldots \lt b_k \leq n$$$, such that for all pairs $$$(i, j)$$$ where $$$1 \leq i \lt j \leq k$$$, the inequality $$$a_{b_i} \oplus a_{b_j} \leq x$$$ is held. Here, $$$\oplus$$$ denotes the bitwise XOR operation. As the answer may be very large, output it modulo $$$998\,244\,353$$$.

Input

The first line of the input contains two integers $$$n$$$ and $$$x$$$ ($$$1 \leq n \leq 150\,000$$$, $$$0 \leq x \lt 2^{30}$$$). Here, $$$n$$$ is the size of the array.

The next line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \leq a_i \lt 2^{30}$$$): the array itself.

Output

Print one integer: the number of non-empty subsets such that the bitwise XOR of every pair of e

Keep XOR Low

Examples