AT_aalc001_b 遅延セグメント木

You are given a sequence of nonnegative integers $ A=(A_1,A_2,\ldots,A_N) $ of length $ N $ . Process $ Q $ queries. Each query is of one of the following $ 2 $ types: - `1 l r x`: For each $ i=l,l+1,\ldots,r $ , add $ x $ to $ A_i $ . - `2 l r`: Print $ \min(A_l,A_{l+1},\ldots,A_r) $ .

The input is given from Standard Input in the following format: > $ N $ $ Q $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $ $ \mathrm{query}_1 $ $ \mathrm{query}_2 $ $ \vdots $ $ \mathrm{query}_Q $ Each query is given in one of the following formats: > $ 1 $ $ l $ $ r $ $ x $ > $ 2 $ $ l $ $ r $

Let $ q $ be the number of type $ 2 $ queries. Print $ q $ lines. The $ j $ -th line should contain the answer to the $ j $ -th type $ 2 $ query.

### Sample Explanation 1 For query $ 1 $ , print $ 3 $ , the minimum of $ A_2,A_3,A_4 $ . Query $ 2 $ changes $ A $ to $ (5,8,12,14,1) $ . For query $ 3 $ , print $ 8 $ , the minimum of $ A_2,A_3,A_4 $ . ### Constraints - $ 1 \leq N \leq 2 \times 10^5 $ - $ 1 \leq Q \leq 2 \times 10^5 $ - $ 0 \leq A_i \leq 10^9 $ - For type $ 1 $ queries, $ 1 \leq l \leq r \leq N $ , $ 0 \leq x \leq 10^9 $ - For type $ 2 $ queries, $ 1 \leq l \leq r \leq N $ - All numerical values in the input are integers.