Given an integer array nums and a positive integer k.

A subsequence sub of nums with length $x$ is defined as valid if the sum of every adjacent pair of elements modulo k is equal. That is:

$(`sub[0]` + `sub[1]`) \pmod{`k`} = (`sub[1]` + `sub[2]`) \pmod{`k`} = \dots = (`sub[x - 2]` + `sub[x - 1]`) \pmod{`k`}$

Return the maximum length of a valid subsequence of nums.

Note: A subsequence is derived from an array by deleting zero or more elements without changing the order of the remaining elements.

Constraints:

• $2 \leq$ nums.length $\leq 10^3$

• $1 \leq$ nums[i] $\leq 10^7$

• $1 \leq$ k $\leq 10^3$

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