Problem: Phoenix has decided to become a scientist! He is currently investigating the growth of bacteria.

Initially, on day 1, there is one bacterium with mass 1.

Every day, some number of bacteria will split (possibly zero or all). When a bacterium of mass m splits, it becomes two bacteria of mass m/2 each. For example, a bacterium of mass 3 can split into two bacteria of mass 1.5.

Also, every night, the mass of every bacteria will increase by one.

Phoenix is wondering if it is possible for the total mass of all the bacteria to be exactly n. If it is possible, he is interested in the way to obtain that mass using the minimum possible number of nights. Help him become the best scientist!

Input

The input consists of multiple test cases. The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases.

The first line of each test case contains an integer n (2 ≤ n ≤ 10^9) — the sum of bacteria masses that Phoenix is interested in. 

Output

For each test case, if there is no way for the bacteria to exactly achieve total mass n, print -1. Otherwise, print two lines.

The first line should contain an integer d — the minimum number of nights needed.

The next line should contain d integers, with the i-th integer representing the number of bacteria that should split on the i-th day.

If there are multiple solutions, print any.

Example

Input


3
9
11
2


Output


3
1 0 2 
3
1 1 2
1
0 

Note

In the first test case, the following process results in bacteria with total mass 9: 

  * Day 1: The bacterium with mass 1 splits. There are now two bacteria with mass 0.5 each. 
  * Night 1: All bacteria's mass increases by one. There are now two bacteria with mass 1.5. 
  * Day 2: None split. 
  * Night 2: There are now two bacteria with mass 2.5. 
  * Day 3: Both bacteria split. There are now four bacteria with mass 1.25. 
  * Night 3: There are now four bacteria with mass 2.25. 

The total mass is 2.25+2.25+2.25+2.25=9. It can be proved that 3 is the minimum number of nights needed. There are also other ways to obtain total mass 9 in 3 nights.

 

In the second test case, the following process results in bacteria with total mass 11: 

  * Day 1: The bacterium with mass 1 splits. There are now two bacteria with mass 0.5. 
  * Night 1: There are now two bacteria with mass 1.5. 
  * Day 2: One bacterium splits. There are now three bacteria with masses 0.75, 0.75, and 1.5. 
  * Night 2: There are now three bacteria with masses 1.75, 1.75, and 2.5. 
  * Day 3: The bacteria with mass 1.75 and the bacteria with mass 2.5 split. There are now five bacteria with masses 0.875, 0.875, 1.25, 1.25, and 1.75. 
  * Night 3: There are now five bacteria with masses 1.875, 1.875, 2.25, 2.25, and 2.75. 

The total mass is 1.875+1.875+2.25+2.25+2.75=11. It can be proved that 3 is the minimum number of nights needed. There are also other ways to obtain total mass 11 in 3 nights.

 

In the third test case, the bacterium does not split on day 1, and then grows to mass 2 during night 1.

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigInteger;
import java.net.PortUnreachableException;
import java.util.*;

// written by luchy0120

public class Main {
    public static void main(String[] args) throws Exception {

        new Main().run();
    }

    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--;
    }

    int child[];
    int color[],dfn[],low[],stack[],cnt[];
    boolean vis[];
    boolean iscut[];
    int deep,top,n,m,sum,ans;
    List<Integer> g[];
    int root = 0;
    //  无向图的强连通分量
    void tarjanNonDirect(int u1) {

        int stk[] = new int[10001];
        int fatk[] = new int[10001];
        int p = 0;
        stk[p] = u1;
        fatk[p] = -1;
        p= 1;
        ot: while(p>0) {
            int u  = stk[p-1];
            int fa = fatk[p-1];


            if(dfn[u]==0) {
                low[u] = dfn[u] = ++deep;
            }
            // stack[top++] = u;

            for (; h[u] != -1; h[u] = ne[h[u]]) {
                int v = to[h[u]];
                if (dfn[v] == 0) {
                    //tarjanNonDirect(v);

                    fatk[p] = u;
                    stk[p++] = v;
                    continue ot;
                } else {
                    low[u] = Math.min(low[u], dfn[v]);
                    // 没有特判是否直接指向父亲
                    // 回边，使用dfn【v】更新low【u】,因为可能是指向父亲，而父亲的low可能比较小
                }
            }
            --p;

            if (fa != -1) {
                low[fa] = Math.min(low[fa], low[u]);
                if (low[u] >= dfn[fa]) {
                    if (fa != root || ++child[fa] > 1) {     // 不是root，直接记为cut，是root，判断是否有两个儿子
                        iscut[fa] = true;
                    }
                    ++dcc_cnt;
                    // 一个割点可能会被多个点双共享
                    //  int z = -1;
                    //    do {
                    //        z = stack[--top];
                    //      dcc[dcc_cnt].add(z);
                    //    } while(z != v);
                    //   dcc[dcc_cnt].add(u);
                }


            }

        }
    }
    int gd = 0;
    int id =-1;
    int scc_cnt = 0;
    int sccno[];
    // 有向图的强连通分量
    void tarjan(int u) {
        int stk[] = new int[10001];
        //   int tptk[] = new int[10001];

        //  int fatk[] = new int[10001];
        int p  =1; stk[0] = u;//fatk[0] =-1;
        ot:while(p>0) {
            u  = stk[p-1];
            //  int fa  = fatk[p-1];
            if (dfn[u] == 0) {
                low[u] = dfn[u] = ++deep;
                stack[top++] = u;

            }

            for (; hc[u] != -1; hc[u] = ne[hc[u]]) {
                int v = to[hc[u]];
                if (dfn[v] == 0) {
                    stk[p++] = v;
                    continue ot;
                    //  low[u] = Math.min(low[u], low[v]);
                } else if (sccno[v] == 0) {
                    // dfn>0 but sccno==0, means it's in current stack
                    low[u] = Math.min(low[u], low[v]);
                }
            }

            p--;
            if (dfn[u] == low[u]) {
                sccno[u] = ++scc_cnt;
                if(u==1){
                    id = scc_cnt;
                }

                while (stack[top - 1] != u) {
                    sccno[stack[top - 1]] = scc_cnt;
                    if(stack[top - 1]==1){
                        id = scc_cnt;
                    }
                    --top;
                }

                --top;
            }
            if(p>=1){
                int fa = stk[p-1];
                low[fa] = Math.min(low[fa], low[u]);
            }
        }
    }
    int rr =0;
//    void solve() {
//
//    }




//    int get_room(int i,int j){
//        return i/3*3 + j/3;
//    }

//    int a[][] = new int[9][9];
//    int space = 0;
//
//    boolean vis_row[][] = new boolean[9][10];
//    boolean vis_col[][] = new boolean[9][10];
//    boolean vis_room[][] = new boolean[9][10];
//    int val[][][] =new int[9][9][];
//    int prepare[][];
//
//    void dfs(int rt){
//
//    }

    int h[],to[],ne[];int ct =0;
    void add(int u,int v){
        // u--;v--;
        to[ct] = v;
        ne[ct] = h[u];
        h[u] = ct++;

    }

    int dcc_cnt = 0;
    int time = 0;





    long summ[];
    int v[];
    int hc[];
    void solve() {
        int t =ni();
        for(int i=1;i<=t;++i){
            int n = ni();
            List<Integer> li = new ArrayList<>();
            for(int j=1;j<=n;j*=2){
                n -= j;
                li.add(j);
            }
            if(n>0){
                li.add(n);
                Collections.sort(li);
            }
            println(li.size()-1);
            for(int j=1;j<li.size();++j){
                print(li.get(j)-li.get(j-1));
                if(j!=li.size()-1){
                    print(" ");
                }
            }
            println();
        }




//        int n = ni();
//        int m  = n*(n+1)/2;
//        int k = ni();
//        int p = 0;
//
//        double x[] = new double[n];
//        double y[] = new double[n];
//
//        for(int i=0;i<n;++i){
//            x[i] = nd();
//            y[i] = nd();
//        }
//
//        List<Item> li = new ArrayList<>();
//        for(int i=0;i<n;++i){
//            for(int j=i+1;j<n;++j){
//               double r =  (x[i]-x[j])*(x[i]-x[j]) + (y[i]-y[j])*(y[i]-y[j]);
//               li.add(new Item(r,i,j));
//            }
//        }
//        Collections.sort(li,(xx,yy)->Double.compare(xx.s,yy.s));
//
//        init(n + 1);
//
//        int s = 0;
//        int c = n;
//        for (int i = 0; i < li.size(); ++i) {
//            int p1 = li.get(i).a;
//            int p2 = li.get(i).b;
//            if (root(p1) != root(p2)) {
//                combine(p1, p2);
//                c--;
//                if(c==k-1){
//                    print(roundS(Math.sqrt(li.get(i).s),2));
//                    break;
//                }
//            }
//        }

    }
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//    }


    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+p)%p;
        while(n!=0L){
            if((n&1L)==1L){
                res = ((res*temp)%p+p)%p;
            }
            temp = ((temp * temp)%p+p)%p;
            n = n>>1L;
        }
        return res%p;
    }
    public static String roundS(double result, int scale){
        String fmt = String.format("%%.%df", scale);
        return String.format(fmt, result);
    }


//    void solve() {
//
//        for(int i=0;i<9;++i) {
//            for (int j = 0; j < 9; ++j) {
//                int v = ni();
//                a[i][j] = v;
//                if(v>0) {
//                    vis_row[i][v] = true;
//                    vis_col[j][v] = true;
//                    vis_room[get_room(i, j)][v] = true;
//                }else{
//                    space++;
//                }
//            }
//        }
//
//
//        prepare = new int[space][2];
//
//        int p = 0;
//
//        for(int i=0;i<9;++i) {
//            for (int j = 0; j < 9; ++j) {
//                if(a[i][j]==0){
//                    prepare[p][0] = i;
//                    prepare[p][1]= j;p++;
//                    List<Integer> temp =new ArrayList<>();
//                    for(int k=1;k<=9;++k){
//                        if(!vis_col[j][k]&&!vis_row[i][k]&&!vis_room[get_room(i,j)][k]){
//                            temp.add(k);
//                        }
//                    }
//                    int sz = temp.size();
//                    val[i][j] = new int[sz];
//                    for(int k=0;k<sz;++k){
//                        val[i][j][k] = temp.get(k);
//                    }
//                }
//            }
//        }
//        Arrays.sort(prepare,(x,y)->{
//           return Integer.compare(val[x[0]][x[1]].length,val[y[0]][y[1]].length);
//        });
//        dfs(0);
//
//
//
//
//
//
//
//
//
//
//    }




    InputStream is;
    PrintWriter out;

    void run() throws Exception {
        //is = new FileInputStream(new File("C:\\Users\\Luqi\\Downloads\\P3387_9.in"));
        is = System.in;
        out = new PrintWriter(System.out);

        solve();
        out.flush();
    }

    private byte[] inbuf = new byte[1024];
    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 = readByte();
        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();
    }

    void printArray(int a[],int from){
        int l = a.length;
        for(int i=from;i<l;++i){
            print(a[i]);
            if(i!=l-1){
                print(" ");
            }
        }
        println();
    }

    void printArray(long a[],int from){
        int l = a.length;
        for(int i=from;i<l;++i){
            print(a[i]);
            if(i!=l-1){
                print(" ");
            }
        }
        println();
    }
}