Codeforces Round #372 (Div. 2) -- C. Plus and Square Root（找规律枚举）

大体题意：

初始时，你的值是2，你可以按+按钮，会让你的值加上任意一个数k，也可以进行开方操作，当你的x是完全平方数时才可以开方，开方后的数值必须要求是你的等级level的整数倍，求要从1级变到n+1级，在开方之前需要加的数是多少？

大体上是这样，在仔细读读，并不难理解！

思路：

其实输出有很多，我是感觉最后一个样例不错，就按照最后一个样例来求值了！

开始是2，+2后，变成4，开方变成2，等级为2， 2/2 = 1

然后2 + 17*2 = 36，开方后变成6 等级为3，  6/3 = 2

然后6 + 46 * 3 = 144，开方后变成12 等级为4   12/4 = 3

然后12 + 97*4 = 400 开方后变成20 等级为5，  20/5 = 4

。。。。

那么第k项就是

(k*（k+1）* k * ( k + 1 ) - (k-1)*k )/k = k*(k+1)*(k+1) - k + 1

带入即可！

k最大是10W，这个公式不会爆long long！

直接打表输出即可：

#include
#define fi first
#define se second
#define ps push_back
#define mr make_pair
using namespace std;
typedef unsigned long long ll;
//typedef unsigned long long ULL;
const ll maxn = 100000 + 10;
const int inf = 0x3f3f3f3f;
const double eps = 1e-10;
const double pi = acos(-1.0);
ll  ans[maxn];
ll ping(ll x){
	return x*(x+1)*(x+1)-x+1;
}
void init(){
	ans[1] = 2ll;
	for (int i = 2; i < maxn; ++i){
		ll t = ping(i);
		ans[i] = t;
		//cout << t << endl;
	}
	
	
}
int main(){
	init(); 
	int n;
	scanf("%d",&n);
	for (int i = 0; i < n; ++i){
		printf("%I64d\n",ans[i+1]);
	}
	return 0;
} 

C. Plus and Square Root

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.

When ZS the Coder is at level k, he can :

1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '' button. Let the number on the screen be x. After pressing this button, the number becomes . After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when xis a perfect square, i.e. x = m2 for some positive integer m.

Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.

ZS the Coder needs your help in beating the game — he wants to reach level n + 1. In other words, he needs to press the '' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '' button at each level.

Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.

Input

The first and only line of the input contains a single integer n (1 ≤ n ≤ 100 000), denoting that ZS the Coder wants to reach level n + 1.

Output

Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '' button at level i.

Each number in the output should not exceed 1018. However, the number on the screen can be greater than1018.

It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.

Examples

input

3

output

14
16
46

input

2

output

999999999999999998
44500000000

input

4

output

2
17
46
97

Note

In the first sample case:

On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14·1 = 16. Then, ZS the Coder pressed the '' button, and the number became .

After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16·2 = 36. Then, ZS pressed the '' button, levelling up and changing the number into .

After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46·3 = 144. Then, ZS pressed the '' button, levelling up and changing the number into .

Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.

Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10·3 = 36, and when the '' button is pressed, the number becomes  and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.

In the second sample case:

On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998·1 = 1018. Then, ZS the Coder pressed the '' button, and the number became .

After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes109 + 44500000000·2 = 9·1010. Then, ZS pressed the '' button, levelling up and changing the number into .

Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.