AT_abc388_b [ABC388B] Heavy Snake

There are $ N $ snakes. Initially, the thickness of the $ i $ -th snake is $ T_i $ , and its length is $ L_i $ . The weight of a snake is defined as the product of its thickness and length. For each integer $ k $ satisfying $ 1 \leq k \leq D $ , find the weight of the heaviest snake when every snake's length has increased by $ k $ .

The input is given from Standard Input in the following format: > $ N $ $ D $ $ T_1 $ $ L_1 $ $ T_2 $ $ L_2 $ $ \vdots $ $ T_N $ $ L_N $

Print $ D $ lines. The $ k $ -th line should contain the weight of the heaviest snake when every snake's length has increased by $ k $ .

### Sample Explanation 1 When every snake’s length has increased by $ 1 $ , the snakes' weights become $ 12, 10, 10, 11 $ , so print $ 12 $ on the first line. When every snake’s length has increased by $ 2 $ , the snakes' weights become $ 15, 15, 12, 12 $ , so print $ 15 $ on the second line. When every snake’s length has increased by $ 3 $ , the snakes' weights become $ 18, 20, 14, 13 $ , so print $ 20 $ on the third line. ### Constraints - $ 1 \leq N, D \leq 100 $ - $ 1 \leq T_i, L_i \leq 100 $ - All input values are integers.