Sums

Krosh loves holidays because he often receives gifts to celebrate them. On this Knowledge Day, he was fortunate to receive several gifts.

Barash and Losyash visited Krosh to congratulate him. They know that he loves counting, especially adding two numbers.

Barash and Losyash immediately presented their gifts to Krosh. When Krosh opened the gifts, he discovered that they were almost identical. Each gift contained blocks with all numbers from $a$ to $b$ inclusive, with exactly one number written on each block, and every block in both gifts was unique. The only difference was the color of the blocks: Barash's blocks were blue, while Losyash's were red.

After the guests left, Krosh decided to play with the blocks. He thought of two numbers: $c$ and $d$, and wrote them on a piece of paper so as not to forget. He then needed to pick one blue block and one red block such that the sum of the numbers written on those blocks would be between $c$ and $d$, inclusive. He wondered in how many ways this could be done.