| You've managed to become a contestant on the hottest new game show, The Price | |
| is Correct! | |
| After asking you to come on down to the stage, the show's host presents you | |
| with a row of **N** closed boxes, numbered from 1 to **N** in order, each | |
| containing a secret positive integer. A curtain opens to reveal a shiny, new | |
| tricycle — you recognize it as an expensive, top-of-the-line model. | |
| The host then proceeds to explain the rules: you must select a contiguous | |
| sequence of the boxes (boxes a..b, for some 1 ≤ a ≤ b ≤ **N**). Your chosen | |
| boxes will then be opened, and if the sum of the numbers inside is no greater | |
| than the price of the tricycle, you win it! | |
| You'd sure like to win that tricycle. Fortunately, not only are you aware that | |
| its price is exactly **P**, but you've paid off the host to let you in on the | |
| contents of the boxes! You know that each box **i** contains the number | |
| **Bi**. | |
| How many different sequences of boxes can you choose such that you win the | |
| tricycle? Each sequence is defined by its starting and ending box indices (a | |
| and b). | |
| ### Input | |
| Input begins with an integer **T**, the number of times you appear on The | |
| Price is Correct. For each show, there is first a line containing the space- | |
| separated integers **N** and **P**. The next line contains **N** space- | |
| separated integers, **B1** through **BN** in order. | |
| ### Output | |
| For the **i**th show, print a line containing "Case #**i**: " followed by the | |
| number of box sequences that will win you the tricycle. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 40 | |
| 1 ≤ **N** ≤ 100,000 | |
| 1 ≤ **P** ≤ 1,000,000,000 | |
| 1 ≤ **Bi** ≤ 1,000,000,000 | |
| ### Explanation of Sample | |
| In the first case no sequence adds up to more than 50, so all 10 sequences are | |
| winners. In the fourth case, you can select any single box, or the sequences | |
| (1, 2), (1, 3), and (2, 3), for 9 total winning sequences. | |