AT_arc204_d [ARC204D] Favorite Interval

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 $ .

The input is given from Standard Input in the following format: > $ N $ $ L $ $ R $

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.

### Sample Explanation 1 When choosing $ P = (2, 4, 5, 3) $ , perform four operations on $ A = (0, 1, 2, 3, 4, 5) $ as follows. - The remainder when $ P_{0} = 2 $ is divided by $ |A| = 6 $ is $ 2 $ , so remove $ A_{2} = 2 $ from $ A $ . Then, $ A = (A_{0}, A_{1}, A_{2}, A_{3}, A_{4}) = (0, 1, 3, 4, 5) $ . - The remainder when $ P_{1} = 4 $ is divided by $ |A| = 5 $ is $ 4 $ , so remove $ A_{4} = 5 $ from $ A $ . Then, $ A = (A_{0}, A_{1}, A_{2}, A_{3}) = (0, 1, 3, 4) $ . - The remainder when $ P_{2} = 5 $ is divided by $ |A| = 4 $ is $ 1 $ , so remove $ A_{1} = 1 $ from $ A $ . Then, $ A = (A_{0}, A_{1}, A_{2}) = (0, 3, 4) $ . - The remainder when $ P_{3} = 3 $ is divided by $ |A| = 3 $ is $ 0 $ , so remove $ A_{0} = 0 $ from $ A $ . Then, $ A = (A_{0}, A_{1}) = (3, 4) $ . Therefore, the goal can be achieved by setting $ P = (2, 4, 5, 3) $ . It is also acceptable to output $ P = (5, 2, 4, 3) $ . ### 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.