Problem: You are given two integers b and w. You have a chessboard of size 10^9 × 10^9 with the top left cell at (1; 1), the cell (1; 1) is painted white.

Your task is to find a connected component on this chessboard that contains exactly b black cells and exactly w white cells. Two cells are called connected if they share a side (i.e. for the cell (x, y) there are at most four connected cells: (x - 1, y), (x + 1, y), (x, y - 1), (x, y + 1)). A set of cells is called a connected component if for every pair of cells C_1 and C_2 from this set, there exists a sequence of cells c_1, c_2, ..., c_k such that c_1 = C_1, c_k = C_2, all c_i from 1 to k are belong to this set of cells and for every i ∈ [1, k - 1], cells c_i and c_{i + 1} are connected.

Obviously, it can be impossible to find such component. In this case print "NO". Otherwise, print "YES" and any suitable connected component.

You have to answer q independent queries.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 10^5) — the number of queries. Then q queries follow.

The only line of the query contains two integers b and w (1 ≤ b, w ≤ 10^5) — the number of black cells required and the number of white cells required.

It is guaranteed that the sum of numbers of cells does not exceed 2 ⋅ 10^5 (∑ w + ∑ b ≤ 2 ⋅ 10^5).

Output

For each query, print the answer to it.

If it is impossible to find the required component, print "NO" on the first line.

Otherwise, print "YES" on the first line. In the next b + w lines print coordinates of cells of your component in any order. There should be exactly b black cells and w white cells in your answer. The printed component should be connected.

If there are several answers, you can print any. All coordinates in the answer should be in the range [1; 10^9].

Example

Input


3
1 1
1 4
2 5


Output


YES
2 2
1 2
YES
2 3
1 3
3 3
2 2
2 4
YES
2 3
2 4
2 5
1 3
1 5
3 3
3 5

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigInteger;
import java.util.*;
public class Main {
    public static void main(String[] args) throws Exception {
        new Main().run();}

    int n;
    int v[][];
    int lisan(int[][] arr,int idx){
        for(int i=0;i<n;++i){
            v[i][0] = arr[i][idx];
            v[i][1] = i;
        }
        Arrays.sort(v, new Comparator<int[]>() {
            @Override
            public int compare(int[] x, int[] y) {
                return x[0]-y[0];
            }
        });
        int tot = -1;
        for (int i = 0; i < n; ++i) {
            if(i==0||v[i][0]!=v[i-1][0]) tot++;
            arr[v[i][1]][idx] = tot;
        }
        // id range from 0 to tot
        return tot+1;
    }


    long inv(long a, long MOD) {
        //return fpow(a, MOD-2, MOD);
        return a==1?1:(long )(MOD-MOD/a)*inv(MOD%a, MOD)%MOD;
    }


    long C(long n,long m, long MOD) {
        if(m+m>n)m=n-m;
        long up=1,down=1;
        for(long i=0;i<m;i++)
        {
            up=up*(n-i)%MOD;
            down=down*(i+1)%MOD;
        }
        return up*inv(down, MOD)%MOD;
    }

    long[][] mult(long a[][],long b[][], long mod){
        int l1 = a.length;
        int l2 = b.length;
        int l3 = b[0].length;
        long r[][] = new long[l1][l3];
        for(int i=0;i<l1;++i){
            for(int j=0;j<l2;++j){
                for(int k=0;k<l3;++k){
                    r[i][k] = (r[i][k] + a[i][j] * b[j][k])%mod;
                }
            }
        }
        return r;
    }

    long[][] ones(int len){
        long r[][] = new long[len][len];
        for(int i=0;i<len;++i){
            r[i][i] = 1L;
        }
        return r;
    }

    long[][] quick(long a[][], long times,long mod){
        int len = a.length;
        long ans[][] = ones(len);

        while(times>0){
            if((times&1)==1) {
                ans = mult(ans, a, mod);
            }
            a = mult(a, a, mod);
            times >>= 1;
        }

        return ans;
    }


    int[] h,ne,to,q,dis,cur;
    long []val;
    int ct = 0;
    long INF = 233333333333333L;

    void graph(int n,int m){
        h = new int[n];
        Arrays.fill(h,-1);
        ne = new int[2 * m];
        to = new int[2 * m];
        val = new long[2 * m];
        q = new int[n];
        ct = 0;
        dis = new int[n];
    }

    void link(int u,int v,long w){
        to[ct] = v;
        ne[ct] = h[u];
        val[ct] = w;
        h[u] = ct++;

        to[ct] = u;
        ne[ct] = h[v];
        val[ct] = 0;
        h[v] = ct++;

    }

    boolean bfs(int st, int ed){
        int e = 0;
        int s = 0;
        Arrays.fill(dis,-1);
        dis[st] = 0;
        q[e++] = st;
        while(s<e){
            int x = q[s++];
            for(int i=h[x];i!=-1;i=ne[i]){
                int v = to[i];
                if(dis[v]==-1 && val[i]>0L){
                    dis[v] = dis[x] + 1;
                    q[e++] = v;
                }
            }
        }
        return dis[ed]!=-1;
    }

    long dfs(int x,int ed, long maxflow){
        if(x == ed) return maxflow;
        long ans = 0;

        for(int i= cur[x];i!=-1;i=ne[i]){
            if(ans >= maxflow){
                break;
            }
            int v = to[i];
            if(dis[v]!=dis[x]+1 || val[i]==0L ){
                continue;
            }
            cur[x] = i;
            long f = dfs(v, ed, Math.min(val[i], maxflow-ans));
            val[i] -= f;
            val[i^1] += f;
            ans += f;
        }
        if(ans==0) dis[x] = -1;
        return ans;
    }

    long dinic(int st,int ed){
        long ans = 0;
        while(bfs(st,ed)){
            cur = h.clone();
            long k;
            while((k = dfs(st,ed,INF))>0) ans += k;
        }
        return ans;
    }


    int dx[] = {0,1};
    int dy[] = {1,0};
    int res = 0;
    void dfs(int r,int c,int[][] a,int len,int ii)
    {
        int n = a.length;
        for(int d:new int[]{-1,1}){
            int i = (ii + d + 4) % 4;
            int x = r;
            int y = c;
            int sp = 0;
            while(x+dx[i]<n&&x+dx[i]>=0&&y+dy[i]>=0&&y+dy[i]<n&&a[x+dx[i]][y+dy[i]]!=1&&a[x+dx[i]][y+dy[i]]!=2){
                x += dx[i];
                y += dy[i];
                sp++;
                a[x][y] = 2;
            }

            if(x+dx[i]<n&&x+dx[i]>=0&&y+dy[i]>=0&&y+dy[i]<n&&a[x+dx[i]][y+dy[i]]==2){
                res = Math.max(len+sp,res);
            }else if(sp>0){
                dfs(x, y, a, len + sp, i);
            }

            while(!(x==r&&y==c)){
                a[x][y] = 0;
                x -= dx[i];
                y -= dy[i];
            }
        }


    }
    static long mul(long a, long b, long p)
    {
        long res=0,base=a;
        while(b>0)
        {
            if((b&1L)>0)
                res=(res+base)%p;
            base=(base+base)%p;
            b>>=1;
        }
        return res;
    }

    static long mod_pow(long k,long n,long p){
        long res = 1L;
        long temp = k%p;
        while(n!=0L){
            if((n&1L)==1L){
                res = mul(res,temp,p);
            }
            temp = mul(temp,temp,p);
            n = n>>1L;
        }
        return res%p;
    }


    int manacher(String s){
        StringBuilder sb  =new StringBuilder();
        sb.append('#');
        for(int i=0;i<s.length();++i){
            sb.append(s.charAt(i));
            sb.append('#');
        }
        char cs[] = sb.toString().toCharArray();
        int mx = 0; int id = 0;
        int p[] = new int[cs.length]; // r of match
        p[0] = 1;
        for(int i=1;i<cs.length;++i){
            if(mx>i) p[i] = Math.min(p[id*2-i], mx-i);
            else p[i] = 1;
            for(;i+p[i]<cs.length&& i-p[i]>=0 &&cs[i+p[i]]==cs[i-p[i]];p[i]++);
            if(p[i]+i>mx) {
                mx = p[i] + i; id = i;
            }
        }
        int ans = 0;
        for(int i=0;i<cs.length;++i){
            ans = Math.max(ans,p[i]);
        }
        return ans-1;
    }


    boolean next_perm(int[] a){
        int len = a.length;
        for(int i=len-2,j = 0;i>=0;--i){
            if(a[i]<a[i+1]){
                j = len-1;
                for(;a[j]<=a[i];--j);
                int p = a[j];
                a[j] = a[i];
                a[i] = p;
                j = i+1;
                for(int ed = len-1;j<ed;--ed) {
                    p = a[ed];
                    a[ed] = a[j];
                    a[j++] = p;
                }
                return true;
            }
        }
        return false;
    }


    public static String roundS(double result, int scale){
        String fmt = String.format("%%.%df", scale);
        return String.format(fmt, result);
    }

    int zz = 0;
    int mx = 0;

    public static double roundToSignificantFigures(double num, int n) {
        if(num == 0) {
            return 0;
        }

        final double d = Math.ceil(Math.log10(num < 0 ? -num: num));
        final int power = n - (int) d;

        final double magnitude = Math.pow(10, power);
        final long shifted = Math.round(num*magnitude);
        return shifted/magnitude;
    }

    double dis(double x,double y,double x1,double y1){
        return Math.sqrt((x-x1)*(x-x1)+(y-y1)*(y-y1));
    }

    int go(int u,int ch[][], int num[],int comp,int dp){
        if(num[u]<comp) return 0;

        int mx = 0;

        for(int i=0;i<26;++i){
            if(ch[u][i]!=0){
                int r = go(ch[u][i],ch,num,comp,dp+1);
                mx += r;
            }
        }
        mx += num[u]/comp;
        return mx;
    }

    int mid = 0;


    void godeep(int step ,int x,int y,long st,long arr[][], HashMap<Long,Integer> map[][]){
        long cur = st ^ arr[x][y];
        int v = map[x][y].getOrDefault(cur,0);
        map[x][y].put(cur,v + 1);
        if(mid==step){
           return;
        }
        for(int i=0;i<2;++i){
            int nx = x + dx[i];
            int ny = y + dy[i];
            if(nx>=0&&ny>=0&&nx<n&&ny<m) {
                godeep(step + 1, nx, ny, cur , arr,map );
            }
        }
    }

    long result = 0;
    long k  =0;
    void goabove(int step, int x,int y,long st,long arr[][],HashMap<Long,Integer> map[][]){
        if(step==(n+m-mid-2))
        {
            if(map[x][y].containsKey(st^k))
                result += map[x][y].get(st^k);
            return;
        }
        if(x-1>=0)
            goabove(step+1,x-1,y,st^arr[x][y],arr,map);
        if(y-1>=0)
            goabove(step+1, x,y-1,st^arr[x][y],arr,map);
    }

    int m = 0;
    static int groups = 0;
    static int[] fa;
    static int[] sz;

    static void init(int n) {
        groups = n;
        fa = new int[n];
        for (int i = 1; i < n; ++i) {
            fa[i] = i;
        }
        sz = new int[n];
        Arrays.fill(sz, 1);
    }

    static int root(int p) {
        while (p != fa[p]) {
            fa[p] = fa[fa[p]];
            p = fa[p];
        }
        return p;
    }

    static void combine(int p, int q) {
        int i = root(p);
        int j = root(q);
        if (i == j) {
            return;
        }
        if (sz[i] < sz[j]) {
            fa[i] = j;
            sz[j] += sz[i];
        } else {
            fa[j] = i;
            sz[i] += sz[j];
        }
        groups--;
    }
    void solve() {

        int q =ni();
        for(int i=0;i<q;++i){

            int b = ni();
            int w = ni();
            if(w<=b){
                if(w*3+1<b){
                    println("NO");continue;
                }else{
                    println("YES");
                }
                int x = 2; int y = 2;

                for(int j=0;j<w;++j){
                    println(x +" "+y);
                    println(x +" "+(y-1));
                    y += 2;
                }
                y = 2;
                for(int j=0;j<w&&b>w;++j){
                    println(1 +" "+y);
                    --b;y+=2;
                }
                y = 2;
                for(int j=0;j<w&&b>w;++j){
                    println(3 +" "+y);
                    --b;y+=2;
                }
                if(b>w){
                    y--;
                    println(2+" "+y);
                }
            }else{


                if(b*3+1<w){
                    println("NO");continue;
                }else{
                    println("YES");
                }
                int x = 3; int y = 2;

                for(int j=0;j<b;++j){
                    println(x +" "+y);
                    println(x +" "+(y-1));
                    y += 2;
                }
                y = 2;
                for(int j=0;j<b&&b<w;++j){
                    println(2 +" "+y);
                    --w;y+=2;
                }
                y = 2;
                for(int j=0;j<b&&b<w;++j){
                    println(4 +" "+y);
                    --w;y+=2;
                }
                if(b<w){
                    y--;
                    println(3+" "+y);
                }


            }
        }




































//        int n  =ni();
//        int m  =ni();
//
//        long c[][] = new long[1001][1001];
//
//        for(int i=1;i<=1000;++i){
//            c[i][0] = c[i][i] = 1;
//            for(int j=1;j<i;++j){
//                c[i][j] = c[i-1][j] + c[i-1][j-1];
//            }
//        }
//
//        long fact[] = new long[101];
//        fact[0] = 1;
//        for(int i=1;i<=100;++i){
//            fact[i] = fact[i-1]*2L;
//            fact[i] %= 998244353;
//        }
//
//        long dp[] = new long[n+1];
//        for(int i=1;i<=n;++i){
//            dp[i] = dp[i-1] + c[i-1][m-2]*fact[m-2] + c[i-1][m-2]*fact[m-2]*(m-2);
//            dp[i] %= 998244353;
//        }
//        println(dp[n]);












//
//        for(int i=0;i<n;i++) {
//            if(dfn[i]==0) tarjan(i);
//        }
//
//        List<Integer> li[] = new ArrayList[scc_cnt+1];
//
//        for(int i=1;i<=scc_cnt;++i){
//            li[i] = new ArrayList<>();
//        }
//        for(int i=0;i<n;++i){
//            int num = sccno[i];
//            li[num].add(i+1);
//        }
//        int sz = 0;
//        List<Integer> res = new ArrayList<>();
//        for(int i=1;i<=scc_cnt;++i){
//            if(ct1[i]>sz){
//                Collections.sort(li[i]);
//                res = li[i];
//                sz = ct1[i];
//            }else if(ct1[i]==sz){
//                Collections.sort(li[i]);
//                for(int j=0;j<sz;++j){
//                    if(li[i].get(j)<res.get(j)){
//                        res = li[i];break;
//                    }
//                }
//            }
//        }
//        println(sz);
//        for(int u:res){
//            print(u+" ");
//        }


//        int me = sccno[0];
//        in = new boolean[scc_cnt+1];
//
//        graph1(scc_cnt+1, m);
//        graph2(scc_cnt+1, m);
//
//        for(int i=0;i<n;i++) {
//            for(int j=h[i]; j!=-1; j=ne[j]) {
//                int y = to[j];
//                if(sccno[i] != sccno[y]) {
//                    add1(sccno[i],sccno[y]);
//                    add2(sccno[y],sccno[i]); // reverse
//                }
//            }
//        }
//        q = new int[scc_cnt*10];
//        spfa1(me);
//        spfa2(me);
//        int r = ct1[me];
//        for(int i=1;i<=scc_cnt;++i){
//            if(d2[i]==0) continue;
//            for(int j=h1[i];j!=-1;j=ne1[j]){
//                int v = to1[j];
//                if(d1[v]==0) continue;
//                int res = d2[i]  + d1[v] - ct1[me];
//                if(res > r){
//                    r = res;
//                }
//            }
//        }
//        println(r);















//        for(int i=500;i>=100;--i){
//            if(good(i)!=bad(i)){
//                println(good(i));
//                println(bad(i));
//                println(i);
//                println("-----------------------");
//            }
//        }





































        //N , M , K , a , b , c , d

//        int n = ni();
//        int m = ni();
//        int k = ni();
//        int a = ni();
//        int b = ni();
//        int c = ni();
//        int d = ni();
//
//
//        char cc[][] = nm(n,m);
//        char keys[][] = new char[n][m];
//
//        char ky = 'a';
//        for(int i=0;i<k;++i){
//            int x = ni();
//            int y = ni();
//            keys[x][y] = ky;
//            ky++;
//        }
//        int f1[] = {a,b,0};
//
//        int dd[][] = {{0,1},{0,-1},{1,0},{-1,0}};
//
//        Queue<int[]> q =  new LinkedList<>();
//        q.offer(f1);
//        int ts = 1;
//
//        boolean vis[][][] = new boolean[n][m][33];
//
//        while(q.size()>0){
//            int sz = q.size();
//            while(sz-->0) {
//                int cur[] = q.poll();
//                vis[cur[0]][cur[1]][cur[2]] = true;
//
//                int x = cur[0];
//                int y = cur[1];
//
//                for (int u[] : dd) {
//                       int lx = x +  u[0];
//                       int ly = y +  u[1];
//                       if (lx >= 0 && ly >= 0 && lx < n && ly < m && (cc[lx][ly] != '#')&&!vis[lx][ly][cur[2]]){
//                            char ck =cc[lx][ly];
//                            if(ck=='.'){
//                                if(lx==c&&ly==d){
//                                    println(ts); return;
//                                }
//                                if(keys[lx][ly]>='a'&&keys[lx][ly]<='z') {
//                                    int cao = cur[2] | (1 << (keys[lx][ly] - 'a'));
//                                    q.offer(new int[]{lx, ly, cao});
//                                    vis[lx][ly][cao] = true;
//                                }else {
//
//                                    q.offer(new int[]{lx, ly, cur[2]});
//                                }
//
//                            }else if(ck>='A'&&ck<='Z'){
//                                int g = 1<<(ck-'A');
//                                if((g&cur[2])>0){
//                                    if(lx==c&&ly==d){
//                                        println(ts); return;
//                                    }
//                                    if(keys[lx][ly]>='a'&&keys[lx][ly]<='z') {
//
//                                        int cao = cur[2] | (1 << (keys[lx][ly] - 'a'));
//                                        q.offer(new int[]{lx, ly, cao});
//                                        vis[lx][ly][cao] = true;;
//                                    }else {
//
//                                        q.offer(new int[]{lx, ly, cur[2]});
//                                    }
//                                }
//                            }
//                       }
//                }
//
//                }
//            ts++;
//        }
//        println(-1);




//        int n = ni();
//
//        HashSet<String> st = new HashSet<>();
//        HashMap<String,Integer> mp = new HashMap<>();
//
//
//        for(int i=0;i<n;++i){
//            String s  = ns();
//            int id= 1;
//            if(mp.containsKey(s)){
//                int u = mp.get(s);
//                id = u;
//
//            }
//
//            if(st.contains(s)) {
//
//                while (true) {
//                    String ts = s + id;
//                    if (!st.contains(ts)) {
//                        s = ts;
//                        break;
//                    }
//                    id++;
//                }
//                mp.put(s,id+1);
//            }else{
//                mp.put(s,1);
//            }
//            println(s);
//            st.add(s);
//
//        }

//        int t = ni();
//
//        for(int i=0;i<t;++i){
//            int n = ni();
//            long w[] = nal(n);
//
//            Map<Long,Long> mp = new HashMap<>();
//            PriorityQueue<long[]> q =new PriorityQueue<>((xx,xy)->{return Long.compare(xx[0],xy[0]);});
//
//            for(int j=0;j<n;++j){
//                q.offer(new long[]{w[j],0});
//                mp.put(w[j],mp.getOrDefault(w[j],0L)+1L);
//            }
//
//            while(q.size()>=2){
//                long f[] = q.poll();
//                long y1 = f[1];
//                if(y1==0){
//                    y1 = mp.get(f[0]);
//                    if(y1==1){
//                        mp.remove(f[0]);
//                    }else{
//                        mp.put(f[0],y1-1);
//                    }
//                }
//                long g[] = q.poll();
//                long y2 = g[1];
//                if(y2==0){
//                    y2 = mp.get(g[0]);
//                    if(y2==1){
//                        mp.remove(g[0]);
//                    }else{
//                        mp.put(g[0],y2-1);
//                    }
//                }
//                q.offer(new long[]{f[0]+g[0],2L*y1*y2});
//
//            }
//            long r[] = q.poll();
//            println(r[1]);
//
//
//
//
//        }
        //  int o= 9*8*7*6;
        //  println(o);


//       int t = ni();
//       for(int i=0;i<t;++i){
//           long a = nl();
//           int k  = ni();
//           if(k==1){
//               println(a);
//               continue;
//           }
//
//           int f = (int)(a%10L);
//           int s = 1;
//           int j = 0;
//           for(;j<30;j+=2){
//               int u = f-j;
//               if(u<0){
//                   u = 10+u;
//               }
//               s = u*s;
//               s = s%10;
//               if(s==k){
//                   break;
//               }
//           }
//
//           if(s==k) {
//               println(a - j - 2);
//           }else{
//               println(-1);
//           }
//
//
//
//
//       }

//     int m = ni();
//     h = new int[n];
//     to = new int[2*(n-1)];
//     ne = new int[2*(n-1)];
//     wt = new int[2*(n-1)];
//
//     for(int i=0;i<n-1;++i){
//         int u = ni()-1;
//         int v = ni()-1;
//
//     }
        //  long a[] = nal(n);


//        int n = ni();
//        int k = ni();
//        t1 = new long[200002];
//
//        int p[][] = new int[n][3];
//
//        for(int i=0;i<n;++i){
//            p[i][0]  = ni();
//            p[i][1]  = ni();
//            p[i][2]  = i+1;
//        }
//        Arrays.sort(p, new Comparator<int[]>() {
//            @Override
//            public int compare(int[] x, int[] y) {
//                if(x[1]!=y[1]){
//                    return Integer.compare(x[1],y[1]);
//                }
//                return Integer.compare(y[0], x[0]);
//            }
//        });
//
//        for(int i=0;i<n;++i){
//            int ck = p[i][0];
//
//        }

















    }









//    int []h,to,ne,wt;


    //    long t2[];
    void update(long[] t,int i,long v){
        for(;i<t.length;i+=(i&-i)){
            t[i] += v;
        }
    }
    long get(long[] t,int i){
        long s = 0;
        for(;i>0;i-=(i&-i)){
            s += t[i];

        }
        return s;
    }

    int equal_bigger(long t[],long v){
        int s=0,p=0;
        for(int i=Integer.numberOfTrailingZeros(Integer.highestOneBit(t.length));i>=0;--i) {
            if(p+(1<<i)< t.length && s + t[p+(1<<i)] < v){
                v -= t[p+(1<<i)];
                p |= 1<<i;
            }
        }
        return p+1;
    }

    static class S{
        int l = 0;
        int r = 0 ;
        long tot = 0;
        long plus = 0;
        long multi = 1;


        public S(int l,int r) {
            this.l = l;
            this.r = r;
        }
    }

    static S a[];
    static long[] o;

    static void init(long[] f){
        o = f;
        int len = o.length;
        a = new S[len*4];
        build(1,0,len-1);
    }

    static void build(int num,int l,int r){
        S cur = new S(l,r);
        if(l==r){
            a[num] = cur;
            a[num].tot = o[l];
            //  a[num].tot %= p;
            return;
        }else{
            int m = (l+r)>>1;
            int le = num<<1;
            int ri = le|1;
            build(le, l,m);
            build(ri, m+1,r);
            a[num] = cur;
            pushup(num,le,ri);
        }
    }

    static long query(int num,int l,int r){
        if(a[num].l>=l&&a[num].r<=r){
            //   a[num].tot %= p;
            return a[num].tot;
        }else{
            int m = (a[num].l+a[num].r)>>1;
            int le = num<<1;
            int ri = le|1;
            //   pushdown(num, le, ri);
            long res = Long.MIN_VALUE;
            if(l<=m) {
                res = Math.max(res, query(le, l, r));
            }
            if(r>m){
                res = Math.max(res, query(ri, l, r));
            }
            //  pushup(num,le,ri);
            return res;
        }
    }

    static void update(int num,int l,long v){
        if(a[num].l == a[num].r){
            a[num].tot  = v;
        }else{
            int m = (a[num].l+a[num].r)>>1;
            int le = num<<1;
            int ri = le|1;
            // pushdown(num, le, ri);
            if(l<=m){
                update(le, l, v);
            }
            if(l>m){
                update(ri, l, v);
            }
            pushup(num,le,ri);
        }
    }

    static long p;
    static void update1(int num,int l,int r,long v){
        if(a[num].l>=l && a[num].r<=r){
            a[num].tot += v*(a[num].r-a[num].l+1);
            a[num].tot %= p;
            a[num].plus += v;
            a[num].plus %= p;
        }else{
            int m = (a[num].l+a[num].r)>>1;
            int le = num<<1;
            int ri = le|1;
            pushdown(num, le, ri);
            if(l<=m){
                update1(le, l, r, v);
            }
            if(r>m){
                update1(ri, l, r, v);
            }
            pushup(num,le,ri);
        }
    }

    static void update2(int num,int l,int r,long v){
        if(a[num].l>=l && a[num].r<=r){
            a[num].tot *= v;
            a[num].tot %= p;
            a[num].plus *= v;
            a[num].plus %= p;
            a[num].multi *= v;
            a[num].multi %= p;
        }else{
            int m = (a[num].l+a[num].r)>>1;
            int le = num<<1;
            int ri = le|1;
            pushdown(num, le, ri);
            if(l<=m){
                update2(le, l, r, v);
            }
            if(r>m){
                update2(ri, l, r, v);
            }
            pushup(num,le,ri);
        }
    }

    static void pushup(int num,int le,int ri){
        a[num].tot = Math.max(a[le].tot , a[ri].tot);
    }

    static void pushdown(int num,int le,int ri){
        if(a[num].multi!=1) {
            a[le].tot *= a[num].multi;
            a[le].tot %= p;
            a[ri].tot *= a[num].multi;
            a[ri].tot %= p;
            a[le].multi *= a[num].multi;
            a[ri].multi *= a[num].multi;
            a[le].multi %= p;
            a[ri].multi %= p;
            a[le].plus *= a[num].multi;
            a[ri].plus *= a[num].multi;
            a[le].plus %= p;
            a[ri].plus %= p;
            a[num].multi = 1;
        }
        if(a[num].plus!=0) {
            a[le].tot += (a[le].r-a[le].l+1)*a[num].plus;
            a[ri].tot += (a[ri].r-a[ri].l+1)*a[num].plus;
            a[le].tot %= p;
            a[ri].tot %= p;
            a[le].plus += a[num].plus;
            a[ri].plus += a[num].plus;
            a[le].plus %= p;
            a[ri].plus %= p;
            a[num].plus = 0;
        }
    }

    long gcd(long a,long b){ return b==0?a: gcd(b,a%b);}
    int gcd(int a,int b){ return b==0?a: gcd(b,a%b);}
    InputStream is;PrintWriter out;
    void run() throws Exception {is = System.in;
        //   is  = new FileInputStream("C:\\Users\\Luqi\\Downloads\\P3119_6.in");
        out = new PrintWriter(System.out);solve();out.flush();}
    private byte[] inbuf = new byte[2];
    public int lenbuf = 0, ptrbuf = 0;
    private int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {lenbuf = is.read(inbuf);} catch (IOException e) {throw new InputMismatchException();}
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];}
    private boolean isSpaceChar(int c) {return !(c >= 33 && c <= 126);}
    private int skip() {int b;while((b = readByte()) != -1 && isSpaceChar(b));return b;}
    private double nd() {return Double.parseDouble(ns());}
    private char nc() {return (char) skip();}
    private char ncc() {int b;while((b = readByte()) != -1 && !(b >= 32 && b <= 126));return (char)b;}
    private String ns() {int b = skip();StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);b = readByte(); }
        return sb.toString();}
    private char[] ns(int n) {char[] buf = new char[n];int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) { buf[p++] = (char) b;b = readByte(); }
        return n == p ? buf : Arrays.copyOf(buf, p);}
    private String nline() {int b = skip();StringBuilder sb = new StringBuilder();
        while (!isSpaceChar(b) || b == ' ') { sb.appendCodePoint(b);b = readByte(); }
        return sb.toString();}
    private char[][] nm(int n, int m) {char[][] a = new char[n][];for (int i = 0; i < n; i++) a[i] = ns(m);return a;}
    private int[] na(int n) {int[] a = new int[n];for (int i = 0; i < n; i++) a[i] = ni();return a;}
    private long[] nal(int n) { long[] a = new long[n];for (int i = 0; i < n; i++) a[i] = nl();return a;}
    private int ni() { int num = 0, b; boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')){};
        if (b == '-') { minus = true; b = readByte(); }
        while (true) {
            if (b >= '0' && b <= '9') num = (num << 3) + (num << 1) + (b - '0');
            else return minus ? -num : num;
            b = readByte();}}
    private long nl() { long num = 0; int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')){};
        if (b == '-') { minus = true; b = readByte(); }
        while (true) {
            if (b >= '0' && b <= '9')  num = num * 10 + (b - '0');
            else return minus ? -num : num;
            b = readByte();}}
    void print(Object obj){out.print(obj);}
    void println(Object obj){out.println(obj);}
    void println(){out.println();}
}