Dreary Design (Small)

A color is a triple of component values giving the red, green, and blue levels. Each component is an integer from 0 to $K$, inclusive. For example, in the color system with $K = 3$, the triples $(0, 2, 3)$ and $(0, 3, 2)$ are two of the distinct colors.

A color is bland when every pair of its component values differs by at most $V$. In a system with $K = 2$ and $V = 1$, the color $(2, 1, 1)$ is bland: red and green differ by 1, red and blue differ by 1, green and blue differ by 0, and no difference exceeds 1. The color $(2, 1, 0)$ is not bland, because red and blue differ by more than 1.

Turner paints gloomy landscapes and wants a color system with many bland colors in it. Given $K$ and $V$, count the distinct bland colors.

The first line contains the number of test cases $T$. Each of the next $T$ lines contains two space separated integers $K$ and $V$.

Limits

• $1 \le T \le 100$
• $0 \le K \le 255$
• $0 \le V \le 100$
• $V \le K$
• Every answer fits in a signed 32-bit integer.

For each test case, print one line of the form Case #x: y, where $x$ is the test case number starting from 1 and $y$ is the number of distinct bland colors.

With $K = 1$ and $V = 1$ there are eight colors, $(0,0,0)$, $(0,0,1)$, $(0,1,0)$, $(0,1,1)$, $(1,0,0)$, $(1,0,1)$, $(1,1,0)$, and $(1,1,1)$, and all eight are bland, so the answer is 8.

With $K = 1$ and $V = 0$ the same eight colors exist, but only $(0,0,0)$ and $(1,1,1)$ are bland, so the answer is 2.