Educational Codeforces Round 20 A. Maximal Binary Matrix

A. Maximal Binary Matrix

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given matrix with n rows and n columns filled with zeroes. You should put k ones in it in such a way that the resulting matrix is symmetrical with respect to the main diagonal (the diagonal that goes from the top left to the bottom right corner) and is lexicographically maximal.

One matrix is lexicographically greater than the other if the first different number in the first different row from the top in the first matrix is greater than the corresponding number in the second one.

If there exists no such matrix then output -1.

Input

The first line consists of two numbers n and k (1 ≤ n ≤ 100, 0 ≤ k ≤ 106).

Output

If the answer exists then output resulting matrix. Otherwise output -1.

Examples

input

2 1

output

1 0 
0 0 

input

3 2

output

1 0 0 
0 1 0 
0 0 0 

input

2 5

output

-1

---

昨晚模拟的时候脑残了，把这个字典序搞复杂了许多，还有在主对角线填1的时候比较迷。早上一想不就是每行对称先填啊，只要不是1就可以填两个数的，先填主对角线啊填的过程中k的个数是奇数也填啊，最后你怎么搞a[n][n]也是可以填的，巧妙避开了你填错的的问题。随便模拟下就过了。

#include <stdio.h>
int a[105][105];
int main()
{int n,k;
scanf("%d%d",&n,&k);
for(int i=1;i<=n;i++){
if(!k)break;
else{
a[i][i]=1;
k--;
}
for(int j=i+1;j<=n;j++){
if(k<=1)
break;
else{
a[i][j]=a[j][i]=1;
k-=2;
}
}
}
if(k)
printf("-1");
else{
for(int i=1;i<=n;i++){
printf("%d",a[i][1]);
for(int j=2;j<=n;j++)
printf(" %d",a[i][j]);
printf("\n");
}}
return 0;
}