# ---
# title: 1562. Find Latest Group of Size M
# id: problem1562
# author: Tian Jun
# date: 2020-10-31
# difficulty: Medium
# categories: Binary Search
# link: <https://leetcode.com/problems/find-latest-group-of-size-m/description/>
# hidden: true
# ---
# 
# Given an array `arr` that represents a permutation of numbers from `1` to `n`.
# You have a binary string of size `n` that initially has all its bits set to
# zero.
# 
# At each step `i` (assuming both the binary string and `arr` are 1-indexed)
# from `1` to `n`, the bit at position `arr[i]` is set to `1`. You are given an
# integer `m` and you need to find the latest step at which there exists a group
# of ones of length `m`. A group of ones is a contiguous substring of 1s such
# that it cannot be extended in either direction.
# 
# Return _the latest step at which there exists a group of ones of length
# **exactly**_  `m`. _If no such group exists, return_  `-1`.
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: arr = [3,5,1,2,4], m = 1
#     Output: 4
#     Explanation: Step 1: "00 _1_ 00", groups: ["1"]
#     Step 2: "0010 _1_ ", groups: ["1", "1"]
#     Step 3: " _1_ 0101", groups: ["1", "1", "1"]
#     Step 4: "1 _1_ 101", groups: ["111", "1"]
#     Step 5: "111 _1_ 1", groups: ["11111"]
#     The latest step at which there exists a group of size 1 is step 4.
# 
# **Example 2:**
# 
#     
#     
#     Input: arr = [3,1,5,4,2], m = 2
#     Output: -1
#     Explanation: Step 1: "00 _1_ 00", groups: ["1"]
#     Step 2: " _1_ 0100", groups: ["1", "1"]
#     Step 3: "1010 _1_ ", groups: ["1", "1", "1"]
#     Step 4: "101 _1_ 1", groups: ["1", "111"]
#     Step 5: "1 _1_ 111", groups: ["11111"]
#     No group of size 2 exists during any step.
#     
# 
# **Example 3:**
# 
#     
#     
#     Input: arr = [1], m = 1
#     Output: 1
#     
# 
# **Example 4:**
# 
#     
#     
#     Input: arr = [2,1], m = 2
#     Output: 2
#     
# 
# 
# 
# **Constraints:**
# 
#   * `n == arr.length`
#   * `1 <= n <= 10^5`
#   * `1 <= arr[i] <= n`
#   * All integers in `arr` are  **distinct**.
#   * `1 <= m <= arr.length`
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
