砝碼 - Problem

#10515. 砝碼

Statistics

AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

Link 有 $m$ 個砝碼，每個砝碼的重量都是一個正整數。

已知 Link 可以用這些砝碼稱出 $1$ 到 $n$ 中的所有整數重量（砝碼僅能放在天平的同一邊），Link 手上最重的砝碼至少有多重？

注意：Link 手上的砝碼能否表示出 $n + 1$ 或更大的重量是未知的。

輸入格式

每個測試文件包含多組測試數據。第一行包含測試數據的組數 $T$ ($1 \le T \le 2 \times 10^5$)。每組測試數據的格式如下：

第一行包含兩個整數 $n$ 和 $m$ ($1 \le n, m \le 10^9$)，表示砝碼能表示的已知最大重量和砝碼的數量。

輸出格式

對於每組數據，輸出一行一個整數，表示 Link 手上最重的砝碼的重量的最小值。如果不可能用 $m$ 個砝碼表示出 $1$ 到 $n$ 中的所有重量，請輸出 “-1”。

範例

輸入格式 1

2
40 6
16 4

輸出格式 1

13
-1

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