package contest200904; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.ArrayList; import java.util.Arrays; import java.util.Comparator; import java.util.InputMismatchException; import java.util.List; public class F2 { InputStream is; PrintWriter out; String INPUT = ""; void solve() { int n = ni(), m = ni(); int[][] cons = new int[m][]; for(int i = 0;i < m;i++){ cons[i] = new int[]{ni()-1, ni()-1, ni()}; } Arrays.sort(cons, new Comparator() { public int compare(int[] a, int[] b) { return a[1] - b[1]; } }); LST z = new LST(n+1); z.setRange(n+1); for(int i = 0;i < m;i++){ if(cons[i][2] != 0){ for(int j = cons[i][0];j != -1 && j <= cons[i][1];j = z.next(cons[i][0])){ z.unset(j); } } } int[] ls = new int[n]; Arrays.fill(ls, 10); for(int i = 0;i < m;i++){ if(cons[i][2] == 0){ ls[cons[i][1]] = -cons[i][0]; } } SegmentTreeRMQ st = new SegmentTreeRMQ(ls); SegmentTreeRSQ sq = new SegmentTreeRSQ(n+1); // tr(ls); long[] dp = new long[n+2]; int mod = 1000000007; long i2 = invl(2, mod); dp[0] = 1; sq.add(0, (int)(dp[0] * pow(i2, 0, mod) % mod)); int p = 0; for(int i = 1;i <= n+1;i++){ if(!z.get(i-1))continue; int low = -2, high = i-1; while(high - low > 1){ int h = high+low>>1; // tr(h, i, -st.minx(h, i-1), h); if(-st.minx(Math.max(h, 0), i-1) <= h){ high = h; }else{ low = h; } } // tr(i, high); while(p < m && cons[p][1] <= i-1){ if(cons[p][2] != 0){ sq.mul(0, cons[p][0]+1, (int)i2); // tr(cons[p][0], cons[p][1]+1, i2); } p++; } dp[i] = sq.sum(high+1, i) * pow(2, i-1, mod) % mod; if(i <= n)sq.add(i, (int)(dp[i] * pow(i2, i, mod) % mod)); } // tr(z); // tr(dp); out.println(dp[n+1]); } public static long invl(long a, long mod) { long b = mod; long p = 1, q = 0; while (b > 0) { long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; } return p < 0 ? p + mod : p; } public static class SegmentTreeRSQ { public int M, H, N; public long[] st; public long[] muls; int mod = 1000000007; public SegmentTreeRSQ(int n) { N = n; M = Integer.highestOneBit(Math.max(N-1, 1))<<2; H = M>>>1; st = new long[M]; muls = new long[H]; Arrays.fill(muls, 1); } public SegmentTreeRSQ(int[] a) { N = a.length; M = Integer.highestOneBit(Math.max(N-1, 1))<<2; H = M>>>1; st = new long[M]; muls = new long[H]; Arrays.fill(muls, 1); for(int i = 0;i < N;i++){ st[H+i] = a[i]; } for(int i = (M>>1)-1;i >= 1;i--){ propagate(i); } } public void add(int pos, int v) { st[H+pos] += v; for(int i = H+pos>>>1;i >= 1;i >>>= 1){ propagate(i); } } private void propagate(int i) { // int count = H/Integer.highestOneBit(i); st[i] = (st[2*i]+st[2*i+1]) * muls[i] % mod; } public void mul(int l, int r, int v) { if(l < r)mul(l, r, v, 0, H, 1); } private void mul(int l, int r, int v, int cl, int cr, int cur) { if(cur >= H){ st[cur] = st[cur] * v % mod; }else if(l <= cl && cr <= r){ muls[cur] = muls[cur] * v % mod; propagate(cur); }else{ int mid = cl+cr>>>1; if(cl < r && l < mid){ mul(l, r, v, cl, mid, 2*cur); } if(mid < r && l < cr){ mul(l, r, v, mid, cr, 2*cur+1); } propagate(cur); } } public long sum(int l, int r) { return sum(l, r, 0, H, 1); } private long sum(int l, int r, int cl, int cr, int cur) { if(l <= cl && cr <= r){ return st[cur]; }else{ long val = 0; int mid = cl+cr>>>1; if(cl < r && l < mid){ val += sum(l, r, cl, mid, 2*cur); } if(mid < r && l < cr){ val += sum(l, r, mid, cr, 2*cur+1); } return val * muls[cur] % mod; } } } public static long pow(long a, long n, long mod) { // a %= mod; long ret = 1; int x = 63 - Long.numberOfLeadingZeros(n); for (; x >= 0; x--) { ret = ret * ret % mod; if (n << 63 - x < 0) ret = ret * a % mod; } return ret; } public static class SegmentTreeRMQ { public int M, H, N; public int[] st; public SegmentTreeRMQ(int n) { N = n; M = Integer.highestOneBit(Math.max(N-1, 1))<<2; H = M>>>1; st = new int[M]; Arrays.fill(st, 0, M, Integer.MAX_VALUE); } public SegmentTreeRMQ(int[] a) { N = a.length; M = Integer.highestOneBit(Math.max(N-1, 1))<<2; H = M>>>1; st = new int[M]; for(int i = 0;i < N;i++){ st[H+i] = a[i]; } Arrays.fill(st, H+N, M, Integer.MAX_VALUE); for(int i = H-1;i >= 1;i--)propagate(i); } public void update(int pos, int x) { st[H+pos] = x; for(int i = (H+pos)>>>1;i >= 1;i >>>= 1)propagate(i); } private void propagate(int i) { st[i] = Math.min(st[2*i], st[2*i+1]); } public int minx(int l, int r){ int min = Integer.MAX_VALUE; if(l >= r)return min; while(l != 0){ int f = l&-l; if(l+f > r)break; int v = st[(H+l)/f]; if(v < min)min = v; l += f; } while(l < r){ int f = r&-r; int v = st[(H+r)/f-1]; if(v < min)min = v; r -= f; } return min; } public int min(int l, int r){ return l >= r ? 0 : min(l, r, 0, H, 1);} private int min(int l, int r, int cl, int cr, int cur) { if(l <= cl && cr <= r){ return st[cur]; }else{ int mid = cl+cr>>>1; int ret = Integer.MAX_VALUE; if(cl < r && l < mid){ ret = Math.min(ret, min(l, r, cl, mid, 2*cur)); } if(mid < r && l < cr){ ret = Math.min(ret, min(l, r, mid, cr, 2*cur+1)); } return ret; } } public int firstle(int l, int v) { if(l >= H)return -1; int cur = H+l; while(true){ if(st[cur] <= v){ if(cur >= H)return cur-H; cur = 2*cur; }else{ cur++; if((cur&cur-1) == 0)return -1; if((cur&1)==0)cur>>>=1; } } } public int lastle(int l, int v) { if(l < 0)return -1; int cur = H+l; while(true){ if(st[cur] <= v){ if(cur >= H)return cur-H; cur = 2*cur + 1; }else{ if((cur&cur-1) == 0)return -1; cur--; if((cur&1)==1)cur>>>=1; } } } } public static class LST { public long[][] set; public int n; // public int size; public LST(int n) { this.n = n; int d = 1; for(int m = n;m > 1;m>>>=6, d++); set = new long[d][]; for(int i = 0, m = n>>>6;i < d;i++, m>>>=6){ set[i] = new long[m+1]; } // size = 0; } // [0,r) public LST setRange(int r) { for(int i = 0;i < set.length;i++, r=r+63>>>6){ for(int j = 0;j < r>>>6;j++){ set[i][j] = -1L; } if((r&63) != 0)set[i][r>>>6] |= (1L<= 0){ for(int i = 0;i < set.length;i++, r=r+63>>>6){ for(int j = 0;j < r+63>>>6;j++){ set[i][j] = 0; } if((r&63) != 0)set[i][r>>>6] &= ~((1L<= 0 && pos < n){ // if(!get(pos))size++; for(int i = 0;i < set.length;i++, pos>>>=6){ set[i][pos>>>6] |= 1L<= 0 && pos < n){ // if(get(pos))size--; for(int i = 0;i < set.length && (i == 0 || set[i-1][pos] == 0L);i++, pos>>>=6){ set[i][pos>>>6] &= ~(1L<= 0 && pos < n && set[0][pos>>>6]<<~pos<0; } public LST toggle(int pos) { return get(pos) ? unset(pos) : set(pos); } public int prev(int pos) { for(int i = 0;i < set.length && pos >= 0;i++, pos>>>=6, pos--){ int pre = prev(set[i][pos>>>6], pos&63); if(pre != -1){ pos = pos>>>6<<6|pre; while(i > 0)pos = pos<<6|63-Long.numberOfLeadingZeros(set[--i][pos]); return pos; } } return -1; } public int next(int pos) { for(int i = 0;i < set.length && pos>>>6 < set[i].length;i++, pos>>>=6, pos++){ int nex = next(set[i][pos>>>6], pos&63); if(nex != -1){ pos = pos>>>6<<6|nex; while(i > 0)pos = pos<<6|Long.numberOfTrailingZeros(set[--i][pos]); return pos; } } return -1; } private static int prev(long set, int n) { long h = set<<~n; if(h == 0L)return -1; return -Long.numberOfLeadingZeros(h)+n; } private static int next(long set, int n) { long h = set>>>n; if(h == 0L)return -1; return Long.numberOfTrailingZeros(h)+n; } @Override public String toString() { List list = new ArrayList(); for(int pos = next(0);pos != -1;pos = next(pos+1)){ list.add(pos); } return list.toString(); } } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } public static void main(String[] args) throws Exception { new F2().run(); } 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 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 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 char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[][] nmi(int n, int m) { int[][] map = new int[n][]; for(int i = 0;i < n;i++)map[i] = na(m); return map; } private int ni() { return (int)nl(); } 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(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }