<p>Given two integer arrays&nbsp;<code>arr1</code> and <code>arr2</code>, return the minimum number of operations (possibly zero) needed&nbsp;to make <code>arr1</code> strictly increasing.</p>

<p>In one operation, you can choose two indices&nbsp;<code>0 &lt;=&nbsp;i &lt; arr1.length</code>&nbsp;and&nbsp;<code>0 &lt;= j &lt; arr2.length</code>&nbsp;and do the assignment&nbsp;<code>arr1[i] = arr2[j]</code>.</p>

<p>If there is no way to make&nbsp;<code>arr1</code>&nbsp;strictly increasing,&nbsp;return&nbsp;<code>-1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> arr1 = [1,5,3,6,7], arr2 = [1,3,2,4]
<strong>Output:</strong> 1
<strong>Explanation:</strong> Replace <code>5</code> with <code>2</code>, then <code>arr1 = [1, 2, 3, 6, 7]</code>.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> arr1 = [1,5,3,6,7], arr2 = [4,3,1]
<strong>Output:</strong> 2
<strong>Explanation:</strong> Replace <code>5</code> with <code>3</code> and then replace <code>3</code> with <code>4</code>. <code>arr1 = [1, 3, 4, 6, 7]</code>.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> arr1 = [1,5,3,6,7], arr2 = [1,6,3,3]
<strong>Output:</strong> -1
<strong>Explanation:</strong> You can&#39;t make <code>arr1</code> strictly increasing.</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= arr1.length, arr2.length &lt;= 2000</code></li>
	<li><code>0 &lt;= arr1[i], arr2[i] &lt;= 10^9</code></li>
</ul>

<p>&nbsp;</p>

class Solution {
public:
    int getBigger(vector<int>&nums, int target)
    {
        int low = 0, high = nums.size() - 1;
        int ans =  -1;
        while(low <= high)
        {
            int mid = low + (high - low) / 2;
            if (nums[mid] <= target) low = mid + 1;
            else 
            {
                ans = nums[mid];
                high = mid - 1;
            }
        }
        return ans;
    }
    int solve(vector<int>&nums1, vector<int>& nums2, map<pair<int, int>, int>&mp, int currIdx, int prev)
    {
        if (currIdx == nums1.size()) return 0;
        if (mp.count({currIdx, prev})) return mp[{currIdx, prev}];
        
        int x = INT_MAX, y = INT_MAX, z = INT_MAX;
        int newCurr = nums1[currIdx], curr = nums1[currIdx];
        if (nums1[currIdx] <= prev)  
        {
            newCurr = getBigger(nums2, prev);
            if (newCurr > prev) 
                x = solve(nums1, nums2, mp, currIdx + 1, newCurr);
            if (x != INT_MAX) x++;
        }
        else  
        {
            y = solve(nums1, nums2, mp, currIdx + 1, curr);
            
            newCurr = getBigger(nums2, prev);
            if (newCurr > prev) 
                z =  solve(nums1, nums2, mp, currIdx + 1, newCurr);
            if (z != INT_MAX) z++;
        }
        return mp[{currIdx, prev}] = min({x, y, z});
    }
    int makeArrayIncreasing(vector<int>& arr1, vector<int>& arr2) 
    {
        sort(arr2.begin(), arr2.end());
        map<pair<int, int>, int>mp;
        int ans = solve(arr1, arr2,mp,  0, -1);
        return (ans == INT_MAX? -1 : ans);
    }
};
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