12588번 - Number Game (Large) 다국어

Arya and Bran are playing a game. Initially, two positive integers A and B are written on a blackboard. The players take turns, starting with Arya. On his or her turn, a player can replace A with A - k*B for any positive integer k, or replace B with B - k*A for any positive integer k. The first person to make one of the numbers drop to zero or below loses.

For example, if the numbers are initially (12, 51), the game might progress as follows:

• Arya replaces 51 with 51 - 3*12 = 15, leaving (12, 15) on the blackboard.
• Bran replaces 15 with 15 - 1*12 = 3, leaving (12, 3) on the blackboard.
• Arya replaces 12 with 12 - 3*3 = 3, leaving (3, 3) on the blackboard.
• Bran replaces one 3 with 3 - 1*3 = 0, and loses.

We will say (A, B) is a winning position if Arya can always win a game that starts with (A, B) on the blackboard, no matter what Bran does.

Given four integers A₁, A₂, B₁, B₂, count how many winning positions (A, B) there are with A₁ ≤ A ≤ A₂ and B₁ ≤ B ≤ B₂.

The first line of the input gives the number of test cases, T. T test cases follow, one per line. Each line contains the four integers A₁, A₂, B₁, B₂, separated by spaces.

Limits

• 1 ≤ T ≤ 100. 
• 1 ≤ A₁ ≤ A₂ ≤ 1,000,000.
• 1 ≤ B₁ ≤ B₂ ≤ 1,000,000.
• A₂ - A₁ ≤ 999,999.
• B₂ - B₁ ≤ 999,999.

For each test case, output one line containing "Case #x: y", where x is the case number (starting from 1), and y is the number of winning positions (A, B) with A₁ ≤ A ≤ A₂ and B₁≤ B ≤ B₂.