Bob decided to open a bakery. On the opening day, he baked $$$n$$$ buns that he can sell. The usual price of a bun is $$$a$$$ coins, but to attract customers, Bob organized the following promotion:

Bob chooses some integer $$$k$$$ ($$$0 \le k \le \min(n, b)$$$).
Bob sells the first $$$k$$$ buns at a modified price. In this case, the price of the $$$i$$$-th ($$$1 \le i \le k$$$) sold bun is $$$(b - i + 1)$$$ coins.
The remaining $$$(n - k)$$$ buns are sold at $$$a$$$ coins each.

Note that $$$k$$$ can be equal to $$$0$$$. In this case, Bob will sell all the buns at $$$a$$$ coins each.

Help Bob determine the maximum profit he can obtain by selling all $$$n$$$ buns.

Input

Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains three integers $$$n$$$, $$$a$$$, and $$$b$$$ ($$$1 \le n, a, b \le 10^9$$$) — the number of buns, the usual price of a bun, and the price of the first bun to be sold at a modified price.

Output

For each test case, output a single integer — the maximum profit that Bob can obtain.

Note

In the first test case, it is optimal for Bob to choose $$$k = 1$$$. Then he will sell one bun for $$$5$$$ coins, and three buns at the usual price for $$$4$$$ coins each. Then the profit will be $$$5 + 4 + 4 + 4 = 17$$$ coins.

In the second test case, it is optimal for Bob to choose $$$k = 5$$$. Then he will sell all the buns at the modified price and obtain a profit of $$$9 + 8 + 7 + 6 + 5 = 35$$$ coins.

In the third test case, it is optimal for Bob to choose $$$k = 0$$$. Then he will sell all the buns at the usual price and obtain a profit of $$$10 \cdot 10 = 100$$$ coins.

New Bakery

Examples