josephus I done but II is not that easy

CSES - CSES Problem Set/Josephus_Problem_II.cpp

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+//  Josephus Problem II
+
+#include<bits/stdc++.h>
+//There are Solution with sqrt decomposition and segment trees
+using namespace std;
+
+int main() {
+    ios::sync_with_stdio(0);
+    cin.tie(0);
+    cout.tie(0);
+    int n, k; cin >> n >> k;
+    set<int> children;
+    for (int i = 1; i <= n; i++) children.insert(i);
+
+    int i = (k % children.size());
+    while (!children.empty()) {
+        cout << *children.begin() + i <<  " ";
+        children.erase(children.begin() + i);
+//        cout << "S: "<< children.size() << endl;
+        if (!children.empty()) i = (i + k) % children.size();
+    }
+    return 0;
+}