Problem Statement 問題陳述

Alice and Bob are going to play a famous game called Nim.
愛麗絲和鮑勃將要玩一個著名的游戲叫尼姆。
In the game Nim, first they set up stones in K piles containing a₁,…,a_K stones respectively.
在尼姆游戲中，首先在K堆中分別設(shè)置了包含a₁,…,a_K的石頭。
Then they alternatively take turns (Alice moves first).
然后他們輪流移動（愛麗絲先移動）。
On a player’s turn the player chooses a pile and takes some (at least one) stones from that pile.
輪到玩家時，玩家選擇一堆石頭，從那堆石頭中取出一些（至少一塊）。
If there are no piles left which contain any stones, the player loses.
如果沒有剩余的包含任何石頭的樁，玩家將失敗。

Since they like prime numbers very much, they decided to make each a_i a prime number less than or equal to L.
因為他們非常喜歡素數(shù)，所以他們決定使每個a_i都成為小于或等于L的素數(shù)。
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.
給定k和l返回允許Bob獲勝的初始設(shè)置的數(shù)量，假設(shè)它們發(fā)揮的最佳，模100000000007。

Definition 定義

Class: Nim
類別：尼姆
Method: count
方法：計數(shù)
Parameters: int, int
參數(shù)：int，int
Returns: int
返回：int
Method signature: int count(int K, int L)
方法簽名：int count（int k，int l）
(be sure your method is public)
（確保您的方法是公開的）

Notes 筆記

• 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).
• 如果兩個設(shè)置之間至少有一個AI不同（例如，（A1、A2、A3）=（2、5、7）和（2、7、5）視為不同），則認為兩個設(shè)置不同。

Constraints 約束條件

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

Examples 樣例

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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