DSAhardArrays~40m

chmod -R

Problem

You are building a Windows file system permission manager. Files are indexed 0 to n-1, each with a permission value. The system must support two operations efficiently:

["update", l, r, val]: Set the permission of all files in range [l, r] to val (bulk chmod).
["query", l, r]: Return the sum of permissions of all files in range [l, r] (audit report).

Both operations must run in O(log n) time. A naive O(n) scan per operation will time out on large file systems.

Given the initial permission array and a list of operations, return the results. Update operations return null.

Examples

Example 1

Input: (5, [1,2,3,4,5], [["update",0,4,7],["query",0,4]])

Output: [null, 35]

Set all 5 files to permission 7. Sum = 7×5 = 35.

Example 2

Input: (5, [5,5,5,5,5], [["update",1,3,0],["query",0,4]])

Output: [null, 10]

Set files 1-3 to permission 0. Remaining: files 0 and 4 still have permission 5. Sum = 5+0+0+0+5 = 10. Critical: lazy=0 must not be treated as no-op.

Example 3

Input: (5, [1,2,3,4,5], [["update",0,4,10],["update",1,3,20],["update",2,2,30],["query",0,4]])

Output: [null, null, null, 90]

Stacked updates: final array is [10,20,30,20,10]. Sum = 90. Tests propagation order.

Constraints

›1 <= n <= 10^5
›0 <= initial[i] <= 100
›0 <= val <= 100
›0 <= l <= r < n
›At most 10^4 operations

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