B. Levko and Permutation
time limit per test1 second
memory limit per test256 megabytes
inputstandard input
outputstandard output
Levko loves permutations very much. A permutation of length n is a sequence of distinct positive integers, each is at most n.
Let’s assume that value gcd(a, b) shows the greatest common divisor of numbers a and b. Levko assumes that element pi of permutation p1, p2, … , pn is good if gcd(i, pi) > 1. Levko considers a permutation beautiful, if it has exactly k good elements. Unfortunately, he doesn’t know any beautiful permutation. Your task is to help him to find at least one of them.
Input
The single line contains two integers n and k (1 ≤ n ≤ 105, 0 ≤ k ≤ n).
Output
In a single line print either any beautiful permutation or -1, if such permutation doesn’t exist.
If there are multiple suitable permutations, you are allowed to print any of them.
Examples
input
4 2
output
2 4 3 1
input
1 1
output
-1
Note
In the first sample elements 4 and 3 are good because gcd(2, 4) = 2 > 1 and gcd(3, 3) = 3 > 1. Elements 2 and 1 are not good because gcd(1, 2) = 1 and gcd(4, 1) = 1. As there are exactly 2 good elements, the permutation is beautiful.
The second sample has no beautiful permutations.
题意:有 n 个数,从 1 - n 排序,若其数值与位置的最大公因数大于 1 ,则为 good ,现要求这串数中只能有 k 个 good 的数。
AC代码思路:易知,相邻两个数的最大公因数只能是 1 。所以,调换两相邻数的位置,可以减少 2 个 good 。三点注意:1) 当 k 为单数时, n-1 也为单数时,和 n-1 为双数时。
2) 当 k 为双数时, n-1 为单数,和 n-1 为双数。3) n-1
#include
using namespace std;
int main()
{
int n,k;
cin>>n>>k;
if (n-1return cout<<-1,0;
int tm=(n-1-k)/2;
if (!k)
{
if ((n-1)%2)
{
cout<" ";
for (int i=2;i<=n-1;i++)
{
cout<1<<" "<" ";i++;
}
cout<<1;
}
else
{
cout<<1<<" ";
for (int i=2;i<=n;i++)
{
cout<1<<" "<" ";i++;
}
}
}
else {
if ((n-1)%2)
{
if (k%2)
{
cout<<1<<" ";
for (int i=2;i<=n-1;i++)
{
if (tm>0) {cout<1<<" "<" ";i++;tm--;}
else cout<" ";
}
cout<else
{
cout<" ";
for (int i=2;i<=n-1;i++)
{
if (tm>0) {cout<1<<" "<" ";i++;tm--;}
else cout<" ";
}
cout<<1;
}
}
else
{
if (k%2)
{
cout<" ";
for (int i=2;i<=n-1;i++)
{
if (tm>0) {cout<1<<" "<" ";i++;tm--;}
else cout<" ";
}
cout<<1;
}
else
{
cout<<1<<" ";
for (int i=2;i<=n-1;i++)
{
if (tm>0) {cout<1<<" "<" ";i++;tm--;}
else cout<" ";
}
cout<