If a number $a$ is divisible by a number $b$, then $b$ is called a divisor of $a$. A divisor that is common to two integers is called a common divisor of these two numbers, and the largest of these is called the greatest common divisor. For example, the common divisors of 12 and 16 are 1, 2, and 4, the largest of which is 4; thus, 4 is the greatest common divisor of 12 and 16, generally denoted as $\gcd(12, 16) = 4$.

Now, Xiao C gives you two positive integers $n$ and $k$. Please select exactly $k$ distinct positive integers $x_1, x_2, \dots, x_k$ from $[1, n]$ such that $\gcd(x_i, x_j) = 1$ holds for any pair of integers $(i, j)$ where $1 \le i < j \le k$, or determine that no such solution exists.

Input

A single line containing two positive integers $n, k$ ($2 \le k \le n \le 3 \times 10^5$).

Output

If a feasible solution exists, output two lines. The first line should output YES, and the second line should output $k$ distinct positive integers $x_1, x_2, \dots, x_k$ from $[1, n]$. If there are multiple feasible solutions, output any one of them.

If no feasible solution exists, output a single line NO.

Examples

Input 1

3 3

Output 1

YES
1 2 3

Input 2

4 2

Output 2

YES
1 4