Problem: Consider placing N flags on a line. Flags are numbered through 1 to N.

Flag i can be placed on the coordinate X_i or Y_i. For any two different flags, the distance between them should be at least D.

Decide whether it is possible to place all N flags. If it is possible, print such a configulation.

Constraints

* 1 \leq N \leq 1000
* 0 \leq D \leq 10^9
* 0 \leq X_i < Y_i \leq 10^9
* All values in Input are integer.

Input

Input is given from Standard Input in the following format:


N D
X_1 Y_1
X_2 Y_2
\vdots
X_N Y_N


Output

Print `No` if it is impossible to place N flags.

If it is possible, print `Yes` first. After that, print N lines. i-th line of them should contain the coodinate of flag i.

Examples

Input

3 2
1 4
2 5
0 6


Output

Yes
4
2
0


Input

3 3
1 4
2 5
0 6


Output

No

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(ll i=0;i<n;i++)
#define repl(i,l,r) for(ll i=(l);i<(r);i++)
#define per(i,n) for(ll i=n-1;i>=0;i--)
#define perl(i,r,l) for(ll i=r-1;i>=l;i--)
#define fi first
#define se second
#define pb push_back
#define ins insert
#define pqueue(x) priority_queue<x,vector<x>,greater<x>>
#define all(x) (x).begin(),(x).end()
#define CST(x) cout<<fixed<<setprecision(x)
#define vtpl(x,y,z) vector<tuple<x,y,z>>
#define rev(x) reverse(x);
using ll=long long;
using vl=vector<ll>;
using vvl=vector<vector<ll>>;
using pl=pair<ll,ll>;
using vpl=vector<pl>;
using vvpl=vector<vpl>;
const ll MOD=1000000007;
const ll MOD9=998244353;
const int inf=1e9+10;
const ll INF=4e18;
const ll dy[8]={1,0,-1,0,1,1,-1,-1};
const ll dx[8]={0,-1,0,1,1,-1,1,-1};
template<class T> inline bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template<class T> inline bool chmax(T& a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}


struct SCC{
    int n;
    vector<vector<int>> g,rg;
    vector<int> vs,cmp;
    vector<bool> used;
    SCC(int _n){
        n=_n;
        g=vector<vector<int>>(n);rg=g;
        cmp=vector<int>(n);used=vector<bool>(n);
    }
    void add_edge(int f, int t){
        g[f].push_back(t);
        rg[t].push_back(f);
    }
    int init(){
        rep(i,n)if(!used[i])dfs(i);
        int k=0;
        used=vector<bool>(n,false);
        per(i,n){
            if(!used[vs[i]]){
                rdfs(vs[i],k);
                k++;
            }
        }
        return k;
    }
    private:
    void dfs(int v){
        used[v]=true;
        rep(i,g[v].size()){
            if(!used[g[v][i]])dfs(g[v][i]);
        }
        vs.push_back(v);
    }
    void rdfs(int v, int k){
        used[v]=true;cmp[v]=k;
        rep(i,rg[v].size()){
            if(!used[rg[v][i]]){
                rdfs(rg[v][i],k);
            }
        }
    }
};

int main(){
    ll n,d;cin >> n >>d;
    SCC g(2*n);
    vl x(n),y(n);rep(i,n)cin >> x[i] >> y[i];
    rep(i,n){
        repl(j,i+1,n){
            if(abs(x[i]-x[j])<d){
                g.add_edge(i,j+n);
                g.add_edge(j,i+n);

            }
            if(abs(x[i]-y[j])<d){
                g.add_edge(i,j);
                g.add_edge(j+n,i+n);
            }
            if(abs(y[i]-x[j])<d){
                g.add_edge(i+n,j+n);
                g.add_edge(j,i);
            }
            if(abs(y[i]-y[j])<d){
                g.add_edge(i+n,j);
                g.add_edge(j+n,i);
            }
        }
    }
    g.init();
    bool ok=true;
    rep(i,n){
        if(g.cmp[i]==g.cmp[i+n])ok=false;
    }
    if(ok){
        cout << "Yes" <<endl;
        rep(i,n){
            if(g.cmp[i]>g.cmp[i+n])cout << x[i] <<endl;
            else cout << y[i] <<endl;
        }
    }
    else{
        cout << "No" <<endl;
    }
}