CF1978B New Bakery

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.

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.

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

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.