Codeforces Round #642 (Div. 3) A Most Unstable Array

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 ∑i=1n−1|ai−ai+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.

Input
The first line of the input contains one integer t (1≤t≤104) — the number of test cases. Then t test cases follow.

The only line of the test case contains two integers n and m (1≤n,m≤109) — the length of the array and its sum correspondingly.

Output
For each test case, print the answer — the maximum possible value of ∑i=1n−1|ai−ai+1| for the array a consisting of n non-negative integers with the sum m.

Example
inputCopy
5
1 100
2 2
5 5
2 1000000000
1000000000 1000000000
outputCopy
0
2
10
1000000000
2000000000
Note
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.

给定一个n,和一个m,要求构造一个长度为n的数组arr,且arr的求和等于m
求使得 ${\sum }_{i=1}^{n-1}(\mid a_i-a_{i+1}\mid )$∑i=1n−1​(∣ai​−ai+1​∣) 最大
例如: n=5 m=5, 可以构造出arr={0, 2, 0, 3, 0},
分三种情况

1. n==1 , 只能构造出arr={m} 所以 $ans=0$ans=0
2. n==2 只能构造出 $arr=\{0,m\}$arr={0,m}或 $arr=\{m,0\}$arr={m,0}, 所以 $ans=m$ans=m
3. n>=3 可以构造出 $arr=\{0,X,0,Y,0,Z\}$arr={0,X,0,Y,0,Z}等等,每个数字可以贡献左右两次

//#define debug
#ifdef debug
#include <time.h>
#include "/home/majiao/mb.h"
#endif
 
 
#include <iostream>
#include <algorithm>
#include <vector>
#include <string.h>
#include <map>
#include <set>
#include <math.h>
#include <stack>
#include <queue>
#define MAXN (64)
#define ll long long int
#define QAQ (0)
 
using namespace std;
 
int n, m;
int a[MAXN], b[MAXN];
 
int main() {
#ifdef debug
	freopen("test", "r", stdin);
	clock_t stime = clock();
#endif
	int Q;
	scanf("%d ", &Q);
	while(Q--) {
		scanf("%d %d ", &n, &m);
		if(n <= 1) printf("0\n");
		else if(n == 2) printf("%d\n", m);
		else printf("%lld\n", ((ll)m)<<1);
	}
 
 
 
#ifdef debug
	clock_t etime = clock();
	printf("rum time: %lf 秒\n",(double) (etime-stime)/CLOCKS_PER_SEC);
#endif 
	return 0;
}