Problem: You've got an array consisting of n integers: a[1], a[2], ..., a[n]. Moreover, there are m queries, each query can be described by three integers li, ri, ki. Query li, ri, ki means that we should add <image> to each element a[j], where li ≤ j ≤ ri.

Record <image> means the binomial coefficient, or the number of combinations from y elements into groups of x elements.

You need to fulfil consecutively all queries and then print the final array.

Input

The first line contains integers n, m (1 ≤ n, m ≤ 105).

The second line contains n integers a[1], a[2], ..., a[n] (0 ≤ ai ≤ 109) — the initial array.

Next m lines contain queries in the format li, ri, ki — to all elements of the segment li... ri add number <image> (1 ≤ li ≤ ri ≤ n; 0 ≤ k ≤ 100).

Output

Print n integers: the i-th number is the value of element a[i] after all the queries. As the values can be rather large, print them modulo 1000000007 (109 + 7).

Examples

Input

5 1
0 0 0 0 0
1 5 0


Output

1 1 1 1 1


Input

10 2
1 2 3 4 5 0 0 0 0 0
1 6 1
6 10 2


Output

2 4 6 8 10 7 3 6 10 15

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.math.BigInteger;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 29);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            CCuriousArray solver = new CCuriousArray();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class CCuriousArray {
        int mod = (int) 1e9 + 7;
        Combination comb = new Combination((int) 2e5, mod);

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.ri();
            int m = in.ri();
            int[] a = in.ri(n);
            int lim = 100;
            long[][] mat = new long[lim + 1][n];
            for (int i = 0; i < m; i++) {
                int l = in.ri() - 1;
                int r = in.ri() - 1;
                int k = in.ri();
                mat[k][l]++;
                if (r + 1 < n) {
                    for (int j = k; j >= 0; j--) {
                        mat[j][r + 1] -= comb.combination(r - l + k - j, k - j);
                    }
                }
            }
            for (int i = lim; i >= 0; i--) {
                for (int j = 0; j < n; j++) {
                    if (i < lim) {
                        mat[i][j] += mat[i + 1][j];
                    }
                    if (j > 0) {
                        mat[i][j] += mat[i][j - 1];
                    }
                    mat[i][j] %= mod;
                }
            }

            for (int i = 0; i < n; i++) {
                long ans = mat[0][i] + a[i];
                if (ans >= mod) {
                    ans -= mod;
                }
                if (ans < 0) {
                    ans += mod;
                }
                out.append(ans).append(' ');
            }
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        public void populate(int[] data) {
            for (int i = 0; i < data.length; i++) {
                data[i] = readInt();
            }
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int ri() {
            return readInt();
        }

        public int[] ri(int n) {
            int[] ans = new int[n];
            populate(ans);
            return ans;
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class Factorial {
        int[] fact;
        int[] inv;
        int mod;

        public int getMod() {
            return mod;
        }

        public Factorial(int[] fact, int[] inv, int mod) {
            this.mod = mod;
            this.fact = fact;
            this.inv = inv;
            fact[0] = inv[0] = 1;
            int n = Math.min(fact.length, mod);
            for (int i = 1; i < n; i++) {
                fact[i] = i;
                fact[i] = (int) ((long) fact[i] * fact[i - 1] % mod);
            }
            inv[n - 1] = BigInteger.valueOf(fact[n - 1]).modInverse(BigInteger.valueOf(mod)).intValue();
            for (int i = n - 2; i >= 1; i--) {
                inv[i] = (int) ((long) inv[i + 1] * (i + 1) % mod);
            }
        }

        public Factorial(int limit, int mod) {
            this(new int[Math.min(limit + 1, mod)], new int[Math.min(limit + 1, mod)], mod);
        }

        public int fact(int n) {
            if (n >= mod) {
                return 0;
            }
            return fact[n];
        }

        public int invFact(int n) {
            if (n >= mod) {
                throw new IllegalArgumentException();
            }
            return inv[n];
        }

    }

    static class Combination implements IntCombination {
        final Factorial factorial;
        int modVal;

        public Combination(Factorial factorial) {
            this.factorial = factorial;
            this.modVal = factorial.getMod();
        }

        public Combination(int limit, int mod) {
            this(new Factorial(limit, mod));
        }

        public int combination(int m, int n) {
            if (n > m || n < 0) {
                return 0;
            }
            return (int) ((long) factorial.fact(m) * factorial.invFact(n) % modVal * factorial.invFact(m - n) % modVal);
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private static final int THRESHOLD = 32 << 10;
        private final Writer os;
        private StringBuilder cache = new StringBuilder(THRESHOLD * 2);

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        private void afterWrite() {
            if (cache.length() < THRESHOLD) {
                return;
            }
            flush();
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput append(long c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput flush() {
            try {
//            boolean success = false;
//            if (stringBuilderValueField != null) {
//                try {
//                    char[] value = (char[]) stringBuilderValueField.get(cache);
//                    os.write(value, 0, cache.length());
//                    success = true;
//                } catch (Exception e) {
//                }
//            }
//            if (!success) {
                os.append(cache);
//            }
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static interface IntCombination {
    }
}