CF1994C Hungry Games

Yaroslav is playing a computer game, and at one of the levels, he encountered $ n $ mushrooms arranged in a row. Each mushroom has its own level of toxicity; the $ i $ -th mushroom from the beginning has a toxicity level of $ a_i $ . Yaroslav can choose two integers $ 1 \le l \le r \le n $ , and then his character will take turns from left to right to eat mushrooms from this subsegment one by one, i.e., the mushrooms with numbers $ l, l+1, l+2, \ldots, r $ . The character has a toxicity level $ g $ , initially equal to $ 0 $ . The computer game is defined by the number $ x $ — the maximum toxicity level at any given time. When eating a mushroom with toxicity level $ k $ , the following happens: 1. The toxicity level of the character is increased by $ k $ . 2. If $ g \leq x $ , the process continues; otherwise, $ g $ becomes zero and the process continues. Yaroslav became interested in how many ways there are to choose the values of $ l $ and $ r $ such that the final value of $ g $ is not zero. Help Yaroslav find this number!

Each test consists of multiple test cases. The first line contains an integer $ t $ ( $ 1 \le t \le 10^{4} $ ) — the number of test cases. Then follows the description of the test cases. The first line of each test case contains two integers $ n $ , $ x $ ( $ 1 \leq n \leq 2 \cdot 10^5, 1 \le x \le 10^9 $ ) — the number of mushrooms and the maximum toxicity level. The second line of each test case contains $ n $ numbers $ a_1, a_2, \ldots, a_n $ ( $ 1 \leq a_i \leq 10^9 $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, output a single number — the number of subsegments such that the final value of $ g $ will not be zero.

In the first test case, the subsegments $ (1, 1) $ , $ (1, 2) $ , $ (1, 4) $ , $ (2, 2) $ , $ (2, 3) $ , $ (3, 3) $ , $ (3, 4) $ and $ (4, 4) $ are suitable. In the second test case, non-zero $ g $ will remain only on the subsegments $ (1, 1) $ and $ (2, 2) $ . In the third test case, on the only possible subsegment, $ g $ will be zero.