Divide the number n as the sum of k different numbers

Question

I have a number n, and I have to split it into k numbers, so that all k numbers are different, the sum of k numbers is n, and k is the maximum. Example, if n is 9, then the answer should be 1,2,6. If n is 15, then the answer should be 1,2,3,4,5.
This is what I tried -

void findNum(int l, int k, vector<int>& s)
{
    if (k <= 2 * l) {
        s.push_back(k);
        return;
    }
    else if (l == 1) {
        s.push_back(l);
        findNum(l + 1, k - 1, s);
    }
    else if(l == 2) {
        s.push_back(l);
        findNum(l + 2, k - 2, s);
    }
    else{
        s.push_back(l);
        findNum(l + 1, k - l, s);
    }

}

Initially, k = n and l = 1. The resulting numbers are stored in s. This solution, although it returns the number n as the sum of k different numbers, but it is not an optimal solution (k is not maximal). An example output for n = 15 is 1,2,4,8. What changes need to be made to get the right result?

Answer 1

. 1 m , sum(1...m) <= n. , m-1. 1 m | m-1.

.

18
1+2+3+4+5 < 18
+6 = 21 > 18
So, answer: 1+2+3+4+(5+6-(21-18))

28
1+2+3+4+5+6+7 = 28
So, answer: 1+2+3+4+5+6+7

( , O (1))

Find k such that, m * (m+1) > 2 * n
Number of terms = m-1
Terms: 1,2,3...m-2,(m-1 + m - (sum(1...m) - n))