#4680. Hdu5332 Test for Rikka

内存限制:64 MiB 时间限制:2 Sec

题目描述

As we know, Rikka is poor at math. At the test, Rikka finds that she cannot even do a single problem. There is one of the insane problems:
Given an integer K, she needs to come up with an n×n 01 matrix A and an integer m which meet B1,n=K, where B=Am.
It is too difficult for Rikka. Can you help her?
输入k,输出一个n*n的有向图,使从1走m条边到n的路径数正好为k

输入格式

The first line of the input is a single integer T (T=40), indicating the number of testcases. 
Each of the next T lines contains one integer K (0≤K≤10^18). 

输出格式

For each testcase, the first line contains two space-separated integers n,m (1≤n,m≤30).
In each of following n lines print n characters (0 or 1) - the matrix A you find.

样例

样例输入


			
1
4

样例输出


			
2 4
11
01

数据范围与提示