Problem:
Score : 300 points

Problem Statement

The problem set at CODE FESTIVAL 20XX Finals consists of N problems.

The score allocated to the i-th (1≦i≦N) problem is i points.

Takahashi, a contestant, is trying to score exactly N points. For that, he is deciding which problems to solve.

As problems with higher scores are harder, he wants to minimize the highest score of a problem among the ones solved by him.

Determine the set of problems that should be solved.

Constraints

1≦N≦10^7

Partial Score

200 points will be awarded for passing the test set satisfying 1≦N≦1000.

Additional 100 points will be awarded for passing the test set without additional constraints.

Input

The input is given from Standard Input in the following format:

N

Output

Among the sets of problems with the total score of N, find a set in which the highest score of a problem is minimum, then print the indices of the problems in the set in any order, one per line.

If there exists more than one such set, any of them will be accepted.

Sample Input 1

4

Sample Output 1

1
3

Solving only the 4-th problem will also result in the total score of 4 points, but solving the 1-st and 3-rd problems will lower the highest score of a solved problem.

Sample Input 2

7

Sample Output 2

1
2
4

The set \{3,4\} will also be accepted.

Sample Input 3

1

Sample Output 3

1

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.NoSuchElementException;
import java.util.Random;
import java.util.Scanner;

class UnionFind{
	int Parent[];
	UnionFind(int n){//Initialize by -1
		Parent=new int[n];
		Arrays.fill(Parent, -1);
	}
	int root(int A) {//In which tree is A?
		if(Parent[A]<0)return A;
		return Parent[A]=root(Parent[A]);
	}
	int size(int A) {//size of tree which is include A
		return -Parent[root(A)];
	}
	boolean connect(int A,int B) {//Connect A and B
		A=root(A);
		B=root(B);
		if(A==B) return false;
		if(size(A)<size(B)) {int C=0;C=B;B=A;A=C;}//SWAP
		Parent[A]+=Parent[B];
		Parent[B]=A;
		return true;
	}
}
public class Main {
	static FastScanner scan=new FastScanner();
	static Scanner scanner=new Scanner(System.in);
	static Random rand=new Random();
	static long mod=1000000007;
	static double eps=1.0E-14;
	static int big=Integer.MAX_VALUE;
	static double PI=3.14159265358979323846262338327950288;
	static long modlcm(long a,long b) {return a*b*modint(gcd(a,b),mod);}
	static long gcd (long a, long b) {return b>0?gcd(b,a%b):a;}
	static long lcm (long a, long b) {return a/gcd(a,b)*b;}
	static int max(int a,int b) {return a>b?a:b;}
	static int min(int a,int b) {return a<b?a:b;}
	static long lmax(long a,long b) {return Math.max(a, b);}
	static long lmin(long a,long b) {return Math.min(a, b);}
	static long factorial(int i) {return i==1?1:i*factorial(i-1);}
	public static void main(String[] args) throws IOException {
		int n=scan.nextInt();
		long sum=0;
		int cnt=1;
		while(sum<n) {
			sum+=cnt;
			cnt++;
		}
		long uo=sum-n;
		for(int i=1;i<cnt;i++) {
			if(i==uo) {}
			else {
				System.out.println(i);
			}
		}
	}
	static int lower_bound(int a[],int key) {
		int ok=-1;
		int ng=a.length;
		while(ng-ok>1) {
			int mid=(ok+ng)/2;
			if(a[mid]>=key) {
				ng=mid;
			}
			else {
				ok=mid;
			}
		}
		return ok;
	}
	static int upper_bound(int a[],int key) {
		int ok=-1;
		int ng=a.length;
		while(ng-ok>1) {
			int mid=(ok+ng)/2;
			if(a[mid]>key) {
				ng=mid;
			}
			else {
				ok=mid;
			}
		}
		return ok;
	}
	static boolean isPrime (long n) {
		if (n==2) return true;
		if (n<2 || n%2==0) return false;
		double d = Math.sqrt(n);
		for (int i=3; i<=d; i+=2)if(n%i==0){return false;}
		return true;
	}
	static int upper_division(int a,int b) {
		if(a%b==0) {
			return a/b;
		}
		else {
			return a/b+1;
		}
	}
	static long lupper_division(long a,long b) {
		if(a%b==0) {
			return a/b;
		}
		else {
			return a/b+1;
		}
	}
	static int[] setArray(int a) {
		int b[]=new int[a];
		for(int i=0;i<a;i++) {
			b[i]=scan.nextInt();
		}
		return b;
	}
	static long[] lsetArray(int a) {
		long b[]=new long[a];
		for(int i=0;i<a;i++) {
			b[i]=scan.nextLong();
		}
		return b;
	}
	static String reverse(String str) {
		char ch[]=new char[str.length()];
		char chch[]=str.toCharArray();
		int a=str.length();
		for(int i=0;i<upper_division(a,2);i++) {
			ch[i]=chch[ch.length-i-1];
			ch[ch.length-1-i]=chch[i];
		}
		return String.valueOf(ch);
	}
	public static void printArray(int[] que) {
		for(int i=0;i<que.length-1;i++) {
			System.out.print(que[i]+" ");
		}
		System.out.println(que[que.length-1]);
	}
	public static int[][] doublesort(int[][]a) {
		Arrays.sort(a,(x,y)->Integer.compare(x[0],y[0]));
		return a;
	}
	public static long[][] ldoublesort(long[][]a) {
		Arrays.sort(a,(x,y)->Long.compare(x[0],y[0]));
		return a;
	}
	static long modpow(long x,long n,long mo) {
		long sum=1;
		while(n>0) {
			if((n&1)==1) {
				sum=sum*x%mo;
			}
			x=x*x%mo;
			n>>=1;
		}
		return sum;
	}
	public static char[] revch(char ch[]) {
		char ret[]=new char[ch.length];
		for(int i=ch.length-1,j=0;i>=0;i--,j++) {
			ret[j]=ch[i];
		}
		return ret;
	}
	public static int[] revint(int ch[]) {
		int ret[]=new int[ch.length];
		for(int i=ch.length-1,j=0;i>=0;i--,j++) {
			ret[j]=ch[i];
		}
		return ret;
	}
	public static void warshall_floyd(int v[][],int n) {
		for(int k=0;k<n;k++)
			for(int i=0;i<n;i++)
				for(int j=0;j<n;j++)
					v[i][j]=min(v[i][j],v[i][k]+v[k][j]);
	}
	public static long modint(long a,long m) {
		long b=m,u=1,v=0;
		while(b!=0) {
			long t=a/b;
			a-=t*b;
			long x=a;
			a=b;
			b=x;

			u-=t*v;
			x=u;
			u=v;
			v=x;
		}
		u%=m;
		if(u<0)u+=m;
		return u;
	}
}
class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		}else{
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
	private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
	public String next() {
		if (!hasNext()) throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext()) throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while(true){
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			}else if(b == -1 || !isPrintableChar(b)){
				return minus ? -n : n;
			}else{
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
		return (int) nl;
	}
	public double nextDouble() { return Double.parseDouble(next());}
}