# Description

$n,k\leqslant 10^5$

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# Description

$n \leqslant 2\times 10^5$

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# Description

$N \leqslant 5 \times 10^5, \ T<2, \ K \leqslant 10^9$

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# Description

Alice想要得到一个长度为$n$的序列，序列中的数都是不超过$m$的正整数，而且这$n$个数的和是$p$的倍数。
Alice还希望，这$n$个数中，至少有一个数是质数。
Alice想知道，有多少个序列满足她的要求。
$1 \leq n \leq 10^{9}, 1 \leq m \leq 2 \times 10^{7}, 1 \leq p \leq 100$

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# Set of Sets

A set of sets $S$ is said to be pairwise disjoint if and only if:

$$\forall X, Y \in \Bbb S: X \ne Y \implies X \cap Y = \varnothing$$

Here, $∩$ denotes intersection, and $\varnothing$ denotes the empty set.

Hence we can say that the elements of $S$ are pairwise disjoint.

# Family of Sets

An indexed family of sets $\left \langle {S_i} \right \rangle_{i \mathop \in I}$ is said to be pairwise disjoint if and only if:

$$\forall i, j \in I: i \ne j \implies S_i \cap S_j = \varnothing$$

Hence the indexed sets $S_i$ themselves, where $i\in I$, are referred to as being pairwise disjoint.

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