Problem:
Score : 400 points

Problem Statement

There are N people standing on the x-axis.
Let the coordinate of Person i be x_i.
For every i, x_i is an integer between 0 and 10^9 (inclusive).
It is possible that more than one person is standing at the same coordinate.

You will given M pieces of information regarding the positions of these people.
The i-th piece of information has the form (L_i, R_i, D_i).
This means that Person R_i is to the right of Person L_i by D_i units of distance, that is, x_{R_i} - x_{L_i} = D_i holds.

It turns out that some of these M pieces of information may be incorrect.
Determine if there exists a set of values (x_1, x_2, ..., x_N) that is consistent with the given pieces of information.

Constraints

1 \leq N \leq 100 000

0 \leq M \leq 200 000

1 \leq L_i, R_i \leq N (1 \leq i \leq M)

0 \leq D_i \leq 10 000 (1 \leq i \leq M)

L_i \neq R_i (1 \leq i \leq M)

If i \neq j, then (L_i, R_i) \neq (L_j, R_j) and (L_i, R_i) \neq (R_j, L_j).

D_i are integers.

Input

Input is given from Standard Input in the following format:

N M
L_1 R_1 D_1
L_2 R_2 D_2
:
L_M R_M D_M

Output

If there exists a set of values (x_1, x_2, ..., x_N) that is consistent with all given pieces of information, print Yes; if it does not exist, print No.

Sample Input 1

3 3
1 2 1
2 3 1
1 3 2

Sample Output 1

Yes

Some possible sets of values (x_1, x_2, x_3) are (0, 1, 2) and (101, 102, 103).

Sample Input 2

3 3
1 2 1
2 3 1
1 3 5

Sample Output 2

No

If the first two pieces of information are correct, x_3 - x_1 = 2 holds, which is contradictory to the last piece of information.

Sample Input 3

4 3
2 1 1
2 3 5
3 4 2

Sample Output 3

Yes

Sample Input 4

10 3
8 7 100
7 9 100
9 8 100

Sample Output 4

No

Sample Input 5

100 0

Sample Output 5

Yes

Solution in C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

int descending_compare(const void *a, const void *b){
    if (*(int*)a > *(int*)b){
        return -1;
    }else if (*(int*)a == *(int*)b){
        return 0;
    }else{
        return 1;
    }
}

int ascending_compare(const void *a, const void *b){
    if (*(int*)a < *(int*)b){
        return -1;
    }else if (*(int*)a == *(int*)b){
        return 0;
    }else{
        return 1;
    }
}


int lower_bound(int *a, int n, int key){
    int left, mid, right;
    left = 0, right = n;
    mid = (left + right)/2;
    while ((left+1 != mid || mid+1 != right) && mid != left){
        if (key > a[mid]){
            left = mid;
        }else{
            right = mid+1;
        }
        mid = (left + right)/2;
    }
    if (a[left] >= key)return left;
    if (a[mid] >= key)return mid;
    if (a[right] >= key)return right;
    return n;
}

//greatest common divisor
unsigned long  gcd(unsigned long x, unsigned long y){
    if (y == 0){ 
        return x;
    }else if (x > y){
        return gcd(y, x % y);
    }else{
        return gcd(x, y % x);
    }
}



long long factorial(int x){
    long long rtn = 1;
    int i;
    for (i = x; i > 1; i--){
        rtn = (rtn*i);
    }
    return rtn;
}
int field[3][101];
int n;
int tmptotal = 0;
int total = 0;

int dfs(int x, int y){
    tmptotal += field[x][y];
    if (x == 2 && y == n){
        if (tmptotal > total){
            total = tmptotal;
        }
        tmptotal -= field[x][y];
        return 0;
    }
    if (y < n){
        dfs(x, y+1);
    }
    if (x < 2){
        dfs(x+1, y);
    }

    tmptotal -= field[x][y];
    return 0;
}

typedef struct{
int L;
int R;
int D;
} choco_t;

int people[100005];
choco_t LRD[200000];

int cmp( const void *p, const void *q ) {
    return ((choco_t*)p)->L - ((choco_t*)q)->L;
}

int main(void){
    for (int i = 0; i < 100005; i++){
        people[i] = -1;
    }
    int n, m;
    scanf("%d %d", &n, &m);
    for (int i = 0; i < m; i++){
        scanf("%d %d %d", &LRD[i].L, &LRD[i].R, &LRD[i].D);
    }
    qsort(LRD, m, sizeof(choco_t), cmp);
    for (int i = 0; i < m; i++){
        if (people[LRD[i].L] == -1 && people[LRD[i].R] == -1){
            for (int i = 0; i < 100005; i++){
                people[i] = -1;
            }
            people[LRD[i].L] = 0;
        }
        if (people[LRD[i].R] == -1){
            people[LRD[i].R] = people[LRD[i].L]+LRD[i].D;
        }
        if (people[LRD[i].L] == -1){
            people[LRD[i].L] = people[LRD[i].R]-LRD[i].D;
        }
        if ((people[LRD[i].R] != -1 && people[LRD[i].R] != people[LRD[i].L]+LRD[i].D) || (people[LRD[i].L] != -1 && people[LRD[i].L] != people[LRD[i].R]-LRD[i].D)){
            printf("No\n");
            return 0;
        }
    }
    printf("Yes\n");
    return 0;
}