题目描述

You are given two integers \( n \) and \( m \) . You have to construct the array \( a \) of length \( n \) consisting of non-negative integers (i.e. integers greater than or equal to zero) such that the sum of elements of this array is exactly \( m \) and the value \( \sum\limits_{i=1}^{n-1} |a_i - a_{i+1}| \) is the maximum possible. Recall that \( |x| \) is the absolute value of \( x \) .

In other words, you have to maximize the sum of absolute differences between adjacent (consecutive) elements. For example, if the array \( a=[1, 3, 2, 5, 5, 0] \) then the value above for this array is \( |1-3| + |3-2| + |2-5| + |5-5| + |5-0| = 2 + 1 + 3 + 0 + 5 = 11 \) . Note that this example doesn't show the optimal answer but it shows how the required value for some array is calculated.

You have to answer \( t \) independent test cases.

给你两个正整数 \(N\) 和 \(M\)。你需要构造一个长度为 \(N\) 的数组\(（a_1~a_N）\)，该数组由非负整数组成（即大于或等于零的整数），该数组的元素之和正好等于 \(M\)，且使得相邻两数差的绝对值之和最大。

例如：\(a=[1,3,2,5,5,0]\)，则相邻两数差的绝对值为 \(|1-3|+|3-2|+|2-5|+|5-5|+|5-0|=11\)，请注意，该示例不是最佳答案，它只是演示如何计算相邻两数差的绝对值之和。

为了测试方便，你只需要输出最大的绝对值之和即可。

格式

输入格式

The first line of the input contains one integer \( t \) ( \( 1 \le t \le 10^4 \) ) — the number of test cases. Then \( t \) test cases follow.

The only line of the test case contains two integers \( n \) and \( m \) ( \( 1 \le n, m \le 10^9 \) ) — the length of the array and its sum correspondingly.

第一行一个整数 \(T（1≤T≤10^4）\)表示测试组数；

下面每组数据一行，两个整数 \(N\) 和 \(M（1≤N,M≤10^9）\)；

输出格式

The first line of the input contains one integer \( t \) ( \( 1 \le t \le 10^4 \) ) — the number of test cases. Then \( t \) test cases follow.

The only line of the test case contains two integers \( n \) and \( m \) ( \( 1 \le n, m \le 10^9 \) ) — the length of the array and its sum correspondingly.

对于每组数据，输出一行，一个整数表示最大绝对值之和即可。

样例1

输入样例1

5
1 100
2 2
5 5
2 1000000000
1000000000 1000000000

输出样例1

0
2
10
1000000000
2000000000

样例解释

In the first test case of the example, the only possible array is \( [100] \) and the answer is obviously \( 0 \) .

In the second test case of the example, one of the possible arrays is \( [2, 0] \) and the answer is \( |2-0| = 2 \) .

In the third test case of the example, one of the possible arrays is \( [0, 2, 0, 3, 0] \) and the answer is \( |0-2| + |2-0| +|0-3| + |3-0| = 10 \) .

第一组：\([100]\)，答案为\(0\)；

第二组：\([2,0]\)，答案为\(2\)；

第三组：\([0,2,0,3,0]\) ，答案为\(10\)；

限制

时间：\(1s\) 空间：\(256M\)

对于 \(100\%\) 的数据：\(1≤T≤10^4；1≤N,M≤10^9\)

来源

地址：\(zloj,J2021\)域
作者：\(jialiang2509\)