I was trying to solve LightOJ 1278 this problem.

Problem statement : **Given an integer N, you have to find the number of ways you can

express N as sum of consecutive integers. You have to use at least two integers.

For example, N = 15 has three solutions, (1+2+3+4+5), (4+5+6), (7+8).**

Test cases : 200 , N <= 10^14

I came up with a O(sqrt(N)) solution like this , Try all possible lengths (length 2 to O(sqrt(N))) .

Code : —

int main()
{
    int tc,cas = 0;
    sfi(tc);
    while(tc--)
    {
        ll N;
        sfl(N);
        int up_b = (sqrt(8*N+1) - 1)/2;
        int ans = 0;
        loop(len,2,up_b)
        {
            if((len&1))
            {
                if(N%len==0)
                    ans++;

            }
            else
            {
                ll temp = N - len/2;
                if(temp!=0 && temp%len==0)
                    ans++;

            }
        }
        CASE(cas);
        pf("%d\n",ans);


    }



    return 0;
}

And I got TLE . I worked with some smaller N s and found out , that for all powers of 2 the answer is 0 , and for other numbers there 's a pattern with power , for example , ans[3] = 1, ans[9] = 2 , ans[27] = 3 . But , I couldn't find a way to exploit this. Need some hints to improve my run time .