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22148_Primesummation

2022-5-16 18:21| 发布者: Hocassian| 查看: 28| 评论: 0|原作者: 肇庆学院ACM合集

摘要:

C:\Users\Administrator\Downloads\2019-10-12-10-14-5-89506150337400-Problem List-采集的数据-后羿采集器.html

Pro.ID

22148

Title

Prime summation

Title链接

http://10.20.2.8/oj/exercise/problem?problem_id=22148

AC

Submit

Ratio

100.00%

时间&空间限制

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)

描述

Any number greater than 1 can be expressed as sum of some primes, and there may be many ways. For example, the number 9 can be expressed in 4 ways, 9 = 7+2 = 5+2+2 = 3+3+3 = 3+2+2+2.

We order the summations in this way: we order the summations according the first summand in decreasing order. If in a tie, we order them according the second summand in decreasing order, etc. Now, in this problem, you are given two number N and K. Your job is to find the total ways to express N as some primes, and the K-th summations to express N.

输入

Input contains two numbers N and K as described above. 2 ≤ N ≤ 200, 1 ≤ K ≤ 10⁹.

Input is ended by N=K=0, which should not be processed.

输出

Description

Any number greater than 1 can be expressed as sum of some primes, and there may be many ways. For example, the number 9 can be expressed in 4 ways, 9 = 7+2 = 5+2+2 = 3+3+3 = 3+2+2+2.

Input

Input contains two numbers N and K as described above. 2 ≤ N ≤ 200, 1 ≤ K ≤ 10⁹.

Input is ended by N=K=0, which should not be processed.

Output

First output the total ways in the first line.

Then in the second line output the K-th summation in the format like this: 9=3+3+3.

If K > the total ways just output the last summation.

Sample Input

9 2
9 9
0 0

Sample Output

4
9=5+2+2
4
9=3+2+2+2

Source