You are given a 0-indexed integer array coins, representing the values of the coins available, and an integer target.
An integer x is obtainable if there exists a subsequence of coins that sums to x.
Return the minimum number of coins of any value that need to be added to the array so that every integer in the range [1, target] is obtainable.
A subsequence of an array is a new non-empty array that is formed from the original array by deleting some (possibly none) of the elements without disturbing the relative positions of the remaining elements.
\n\n\n
Example 1:
\n\n\nInput: coins = [1,4,10], target = 19\nOutput: 2\nExplanation: We need to add coins 2 and 8. The resulting array will be [1,2,4,8,10].\nIt can be shown that all integers from 1 to 19 are obtainable from the resulting array, and that 2 is the minimum number of coins that need to be added to the array. \n\n\n
Example 2:
\n\n\nInput: coins = [1,4,10,5,7,19], target = 19\nOutput: 1\nExplanation: We only need to add the coin 2. The resulting array will be [1,2,4,5,7,10,19].\nIt can be shown that all integers from 1 to 19 are obtainable from the resulting array, and that 1 is the minimum number of coins that need to be added to the array. \n\n\n
Example 3:
\n\n\nInput: coins = [1,1,1], target = 20\nOutput: 3\nExplanation: We need to add coins 4, 8, and 16. The resulting array will be [1,1,1,4,8,16].\nIt can be shown that all integers from 1 to 20 are obtainable from the resulting array, and that 3 is the minimum number of coins that need to be added to the array.\n\n\n
\n
Constraints:
\n\n1 <= target <= 1051 <= coins.length <= 1051 <= coins[i] <= target给你一个下标从 0 开始的整数数组 coins，表示可用的硬币的面值，以及一个整数 target 。
如果存在某个 coins 的子序列总和为 x，那么整数 x 就是一个 可取得的金额 。
返回需要添加到数组中的 任意面值 硬币的 最小数量 ，使范围 [1, target] 内的每个整数都属于 可取得的金额 。
数组的 子序列 是通过删除原始数组的一些（可能不删除）元素而形成的新的 非空 数组，删除过程不会改变剩余元素的相对位置。
\n\n\n\n
示例 1：
\n\n\n输入：coins = [1,4,10], target = 19\n输出：2\n解释：需要添加面值为 2 和 8 的硬币各一枚，得到硬币数组 [1,2,4,8,10] 。\n可以证明从 1 到 19 的所有整数都可由数组中的硬币组合得到，且需要添加到数组中的硬币数目最小为 2 。\n\n\n
示例 2：
\n\n\n输入：coins = [1,4,10,5,7,19], target = 19\n输出：1\n解释：只需要添加一枚面值为 2 的硬币，得到硬币数组 [1,2,4,5,7,10,19] 。\n可以证明从 1 到 19 的所有整数都可由数组中的硬币组合得到，且需要添加到数组中的硬币数目最小为 1 。\n\n
示例 3：
\n\n\n输入：coins = [1,1,1], target = 20\n输出：3\n解释：\n需要添加面值为 4 、8 和 16 的硬币各一枚，得到硬币数组 [1,1,1,4,8,16] 。 \n可以证明从 1 到 20 的所有整数都可由数组中的硬币组合得到，且需要添加到数组中的硬币数目最小为 3 。\n\n
\n\n
提示：
\n\n1 <= target <= 1051 <= coins.length <= 1051 <= coins[i] <= target1. Suppose currently, for a fixed set of the first several coins the smallest integer that we cannot obtain is x + 1, namely we can form all integers in the range [1, x] but not x + 1.",
"If the next unused coin’s value is NOT x + 1 (note the array is sorted), we have to add x + 1 to the array. After this addition, we can form all values from x + 1 to 2 * x + 1 by adding x + 1 in [1, x]'s formations. So now we can form all the numbers of [1, 2 * x + 1]. After this iteration the new value of x becomes 2 * x + 1."
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