AT_abc474_d [ABC474D] Outweigh

There are $ N $ types of stones, $ 1,2,\dots,N $ . Stones of the same type all have the same weight. Takahashi and Aoki have $ A_i $ and $ B_i $ stones of type $ i $ , respectively. Determine whether there exists a sequence of positive integers $ W=(W_1,W_2,\dots,W_N) $ satisfying the following conditions, and if it exists, construct one such sequence. - $ 1 \leq W_i \leq 10^{18} $ - If the weight of a type- $ i $ stone is $ W_i $ , the total weight of the stones Takahashi has is strictly greater than the total weight of the stones Aoki has.

The input is given from Standard Input in the following format: > $ N $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $ $ B_1 $ $ B_2 $ $ \ldots $ $ B_N $

If there exists $ W=(W_1,W_2,\dots,W_N) $ satisfying the conditions, output it in the following format: > Yes $ W_1 $ $ W_2 $ $ \ldots $ $ W_N $ If there is no $ W=(W_1,W_2,\dots,W_N) $ satisfying the conditions, output `No` in one line.

### Sample Explanation 1 If $ W=(4,7,4) $ , the total weight of the stones Takahashi has is $ 4 \times 4 + 7 \times 7 + 4 \times 4=81 $ . The total weight of the stones Aoki has is $ 4 \times 5 + 7 \times 5 + 4 \times 5=75 $ . ### Constraints - $ 1 \leq N \leq 10^5 $ - $ 1 \leq A_i \leq 10^9 $ - $ 1 \leq B_i \leq 10^9 $ - All input values are integers.