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Problem Statement 问题陈述

Alice and Bob are going to play a famous game called Nim.
爱丽丝和鲍勃将要玩一个著名的游戏叫尼姆。
In the game Nim, first they set up stones in K piles containing a₁,…,a_K stones respectively.
在尼姆游戏中，首先在K堆中分别设置了包含a₁,…,a_K的石头。
Then they alternatively take turns (Alice moves first).
然后他们轮流移动（爱丽丝先移动）。
On a player’s turn the player chooses a pile and takes some (at least one) stones from that pile.
轮到玩家时，玩家选择一堆石头，从那堆石头中取出一些（至少一块）。
If there are no piles left which contain any stones, the player loses.
如果没有剩余的包含任何石头的桩，玩家将失败。

Since they like prime numbers very much, they decided to make each a_i a prime number less than or equal to L.
因为他们非常喜欢素数，所以他们决定使每个a_i都成为小于或等于L的素数。
Given K and L return the number of such initial setups which allows Bob to win, assuming they play optimally, modulo 1,000,000,007.
给定k和l返回允许Bob获胜的初始设置的数量，假设它们发挥的最佳，模100000000007。

Definition 定义

Class: Nim
类别：尼姆
Method: count
方法：计数
Parameters: int, int
参数：int，int
Returns: int
返回：int
Method signature: int count(int K, int L)
方法签名：int count（int k，int l）
(be sure your method is public)
（确保您的方法是公开的）

Notes 笔记

• Two setups are considered different if at least one ai is different between them (for example, (a1,a2,a3)=(2,5,7) and (2,7,5) are considered different).
• 如果两个设置之间至少有一个AI不同（例如，（A1、A2、A3）=（2、5、7）和（2、7、5）视为不同），则认为两个设置不同。

Constraints 约束条件

• K will be between 1 and 1000000000(=10⁹), inclusive.
• K包含在1和1000000000之间。
• L will be between 2 and 50000, inclusive.
• L包含在2和50000之间。

Examples 样例

3
7
Returns: 6
Prime numbers <= 7 are 2, 3, 5 and 7. Bob can win if the initial setup is (2,5,7) or its permutation. So return 3! = 6.

4
13
Returns: 120
Bob can win if the initial setup is (p,p,p,p) for some prime p<=13, (p,p,q,q) or its permutation for p<q<=13, or (3,5,11,13) or its permutation. So return 6+(6C2*6)+4!=6+90+24=120.

10
100
Returns: 294844622

123456789
12345
Returns: 235511047
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