Ledger Consistency Check

A merchant has maintained a ledger recording his monthly income for n months. For each month i (where i = 1,2,...,n), the income is given by a_i. When a_i>0, it means the merchant made a profit of a_i yuan, and when a_i<0, it indicates a loss of |a_i| yuan. The total income over a period is defined as the sum of the monthly incomes over that period.

Due to the sensitive nature of the investigation, the inspector, Chà, secretly viewed the ledger on m separate occasions while working for the merchant. Each time she viewed the ledger, she only managed to see the records for a contiguous segment of months and she memorized the total income for that segment. Specifically, for the j^th query she recalls that the sum of the incomes from month l_j to month r_j is s_j (in other words, \(\sum_{i=l_j}^{r_j}a_i = s_j\)).

Your task is to determine whether there exists any sequence \(a_1,a_2,\ldots,a_n\) (with each \(a_i\) being an integer) satisfying all m records. If such a sequence exists, the ledger may be authentic; otherwise, it is definitely fake.

Input constraints:

• The first line contains two integers \(n\) and \(m\) separated by a space.
• Each of the following m lines contains three integers \(l_j\), \(r_j\) and \(s_j\) where \(1 \le l_j \le r_j \le n\) and \(s_j\) is the remembered total income for that period.

Note: You can assume that the values of the integers are such that a valid solution, if it exists, will have all intermediate calculations within the range of standard 32-bit or 64-bit integer arithmetic.

inputFormat

The first line contains two integers \(n\) and \(m\). Then, m lines follow. Each of these lines contains three integers l, r and s, representing that the total income from month l to month r is s.

outputFormat

Output a single line containing YES if there exists an array \(a_1, a_2, \ldots, a_n\) satisfying the m records, and NO otherwise.

sample

4 3
1 2 3
2 4 2
1 4 5

YES