Problem Statement

You are given integers $N, L, R$.

These integers satisfy the following:

• $2 \leq N$
• $0\leq L < R \leq N$
• $(L, R)\neq (0, N)$

Initialize a length-$N$ sequence $A = (A_{0}, A_{1}, \dots , A_{N - 1})$ as $A = (0, 1, \dots, N - 1)$.

Choose a permutation $P = (P_{0}, P_{1}, \dots, P_{N - (R - L) - 1})$ of $(R - L, R - L + 1, \dots , N - 1)$, and perform the following operation for $i = 0, 1, \dots N - (R - L) - 1$ in this order.

• Let $a$ be the remainder when $P_{i}$ is divided by $|A|$, and remove $A_{a}$ from $A$ (after removing an element, the indices of sequence $A$ are renumbered starting from $0$).

Determine whether there exists a $P$ such that $A = (L, L + 1, \dots , R - 1)$ in the end, and if it exists, output one such $P$.

Constraints

• $2\leq N\leq 2\times 10^{5}$
• $0\leq L < R\leq N$
• $(L, R) \neq (0, N)$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N L R

Output

If there is no $P$ that makes $A = (L, L + 1, \dots , R - 1)$, output No.

If it exists, output a solution in the following format:

Yes
P_{0} P_{1} \cdots P_{N - (R - L) - 1}

Formally, output Yes on the first line, and output $P_{0}, P_{1}, \dots , P_{N - (R - L) - 1}$ separated by spaces on the second line.

If there are multiple solutions, any of them will be considered correct.