Problem:
Score : 300 points

Problem Statement

Dolphin resides in two-dimensional Cartesian plane, with the positive x-axis pointing right and the positive y-axis pointing up.

Currently, he is located at the point (sx,sy). In each second, he can move up, down, left or right by a distance of 1.

Here, both the x- and y-coordinates before and after each movement must be integers.

He will first visit the point (tx,ty) where sx < tx and sy < ty, then go back to the point (sx,sy), then visit the point (tx,ty) again, and lastly go back to the point (sx,sy).

Here, during the whole travel, he is not allowed to pass through the same point more than once, except the points (sx,sy) and (tx,ty).

Under this condition, find a shortest path for him.

Constraints

-1000 ≤ sx < tx ≤ 1000

-1000 ≤ sy < ty ≤ 1000

sx,sy,tx and ty are integers.

Input

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

sx sy tx ty

Output

Print a string S that represents a shortest path for Dolphin.

The i-th character in S should correspond to his i-th movement.

The directions of the movements should be indicated by the following characters:

U: Up

D: Down

L: Left

R: Right

If there exist multiple shortest paths under the condition, print any of them.

Sample Input 1

0 0 1 2

Sample Output 1

UURDDLLUUURRDRDDDLLU

One possible shortest path is:

Going from (sx,sy) to (tx,ty) for the first time: (0,0) → (0,1) → (0,2) → (1,2)

Going from (tx,ty) to (sx,sy) for the first time: (1,2) → (1,1) → (1,0) → (0,0)

Going from (sx,sy) to (tx,ty) for the second time: (0,0) → (-1,0) → (-1,1) → (-1,2) → (-1,3) → (0,3) → (1,3) → (1,2)

Going from (tx,ty) to (sx,sy) for the second time: (1,2) → (2,2) → (2,1) → (2,0) → (2,-1) → (1,-1) → (0,-1) → (0,0)

Sample Input 2

-2 -2 1 1

Sample Output 2

UURRURRDDDLLDLLULUUURRURRDDDLLDL

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<cstdio>
#include<queue>
#include<utility>
#include<cstring>
#include<stack>
#include<algorithm>
#include<cmath>
#include<iostream>
#include<map>
#define MAX_N 100001
#define INF_INT 2147483647
#define INF_LL 9223372036854775807
#define REP(i,n) for(int i=0;i<(int)(n);i++)
using namespace std;
typedef long long int ll;
typedef pair<ll,ll> P;
void init(int n);
int find(int n);
void unite(int x,int y);
bool same(int x, int y);
ll bpow(ll,ll,ll);
typedef vector<int> vec;
typedef vector<vec> mat;
mat mul(mat &A,mat &B);
mat pow(mat A,ll n);
int dx[4] = {1,0,0,-1};
int dy[4] = {0,1,-1,0};


bool cmp_P(const P &a,const P &b){
  return a.second < b.second;
}
int main()
{
  int sx,tx,sy,ty;
  cin >> sx >> sy >> tx >> ty;
  REP(i,tx-sx){
    cout << "R";
  }
  REP(i,ty-sy){
    cout << "U";
  }
  REP(i,tx-sx){
    cout << "L";
  }
  REP(i,ty-sy){
    cout << "D";
  }
  //
  cout << "DR";
  REP(i,tx-sx){
    cout << "R";
  }
  REP(i,ty-sy){
    cout << "U";
  }
  cout << "ULUL";
  REP(i,tx-sx){
    cout << "L";
  }
  REP(i,ty-sy){
    cout << "D";
  }
  cout << "DR" << endl;
  return 0;
}

int par[MAX_N];
int ranks[MAX_N];

//n要素で初期化
void init(int n){
  REP(i,n){
    par[i] = i;
    ranks[i] = 0;
  }

}

//木の根を求める
int find(int x){
  if(par[x] == x){
    return x;
  }else{
    return par[x] = find(par[x]);
  }
}

void unite(int x,int y){
  x = find(x);
  y = find(y);
  if(x == y) return ;
  if(ranks[x] < ranks[y]){
    par[x] = y;
  }else{
    par[y] = x;
    if(ranks[x] == ranks[y]) ranks[x]++;
  }
}

bool same(int x, int y){
  return find(x) == find(y);
}

ll bpow(ll a, ll n,ll mod){
  int i = 0;
  ll res=1;
  while(n){
    if(n & 1)
      res = (res*a) % mod;
    a = (a*a) % mod;
    n >>= 1;
  }
  return res;
}
const int MOD = 1000000007;
mat mul(mat &A, mat &B){
  mat C(A.size(),vec(B[0].size()));
    REP(i,A.size())REP(k,B.size())REP(j,B[0].size()){
    C[i][j] = (C[i][j] + A[i][k] * B[k][j]) % MOD;
  }
  return C;
}

mat pow(mat A,ll n)
{
  mat B(A.size(),vec(A.size()));
  REP(i,A.size()){
    B[i][i] = 1;
  }
  while(n > 0){
    if ( n & 1) B = mul(B,A);
    A = mul(A,A);
    n >>= 1;
  }
  return B;
}