One day, she thinks of a special kind of permutation named. n or just report that there is no such permutation.
Kotori is very good at math (really?) and she loves playing with permutations and primes. One day, she thinks of a special kind of permutation named k k co-prime permutation. A permutation p_1,p_2,cdots,p_n p 1 ,p 2 ,⋯,p n of n n is called a k k co-prime permutation of n n if there exists exactly k k integers i i such that 1 le i le n 1≤i≤n and text{gcd}(p_i,i)=1 gcd(p i ,i)=1, where text{gcd}(x,y) gcd(x,y) indicates the greatest common divisor of x x and y y. Given n n and k k, please help Kotori construct a k k co-prime permutation of n n or just report that there is no such permutation. Recall that a permutation of n n is a sequence of length n n containing all integers from 1 1 to n n.
（图片来源网络，侵删）
