Bob's friend's birthday is about to come and so he decided to buy his friend a gift and give it to him on his birthday. But he doesn't have enough money and hence thought that he should save money. Currently he has X rupees. He wants Y rupees for the gift. But there are only Z days left for his friend's birthday ((Z+1)th day is his birthday). Starting from today, he can save i rupee(s) on the ith day (1 rupee on the first day, 2 rupees on the second day and so on) .Determine if he could save enough money so that he could buy a gift for his friend before his birthday.
Input Format
Each test contains multiple test cases. The first line of each test contains the number of test cases T. The description of test cases is given below:
The first and the only line of each test case contains three integers X,Y,Z.
Output Format
Print YES if Bob can buy the gift, otherwise print NO.
Constraints
1≤T≤1000
0≤X,Y,Z≤105
In the first test case, Bob initially doesn't have money and the cost of the gift is 1 rupee. His friend's birthday is 3 days away and hence he can save 1 rupee in the first day and buy the gift. So, we print YES.
In the second test case, Bob initially has 2 rupees and the cost of the gift is 10 rupees. His friend's birthday is 3 days away and hence he can save 6 rupees. So, he'll have 8 rupees in total before his friend's birthday which is not sufficient to buy the gift and so we print NO.
In the third test case, Bob initially has 8 rupees and the cost of the gift is 8 rupees. His friend's birthday is 0 days away which means the birthday is today and Bob cannot save any money. But, since Bob already has enough amount of money to buy the gift, we print YES.
