Problem:
Score : 600 points

Problem Statement

Kenkoooo found a simple connected graph.
The vertices are numbered 1 through n.
The i-th edge connects Vertex u_i and v_i, and has a fixed integer s_i.

Kenkoooo is trying to write a positive integer in each vertex so that the following condition is satisfied:

For every edge i, the sum of the positive integers written in Vertex u_i and v_i is equal to s_i.

Find the number of such ways to write positive integers in the vertices.

Constraints

2 \leq n \leq 10^5

1 \leq m \leq 10^5

1 \leq u_i < v_i \leq n

2 \leq s_i \leq 10^9

If i\neq j, then u_i \neq u_j or v_i \neq v_j.

The graph is connected.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

n m
u_1 v_1 s_1
:
u_m v_m s_m

Output

Print the number of ways to write positive integers in the vertices so that the condition is satisfied.

Sample Input 1

3 3
1 2 3
2 3 5
1 3 4

Sample Output 1

1

The condition will be satisfied if we write 1,2 and 3 in vertices 1,2 and 3, respectively.
There is no other way to satisfy the condition, so the answer is 1.

Sample Input 2

4 3
1 2 6
2 3 7
3 4 5

Sample Output 2

3

Let a,b,c and d be the numbers to write in vertices 1,2,3 and 4, respectively.
There are three quadruples (a,b,c,d) that satisfy the condition:

(a,b,c,d)=(1,5,2,3)

(a,b,c,d)=(2,4,3,2)

(a,b,c,d)=(3,3,4,1)

Sample Input 3

8 7
1 2 1000000000
2 3 2
3 4 1000000000
4 5 2
5 6 1000000000
6 7 2
7 8 1000000000

Sample Output 3

0

Solution in C# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

#region いつもの
using AtCoderProject;
using System;
using System.Collections.Generic;
using System.Linq;
using static AtCoderProject.Global;
using BigInteger = System.Numerics.BigInteger;
using BitOperations = System.Numerics.BitOperations;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using StringBuilder = System.Text.StringBuilder;
using Unsafe = System.Runtime.CompilerServices.Unsafe;

namespace AtCoderProject
{
    using System.IO;
    using System.Text;
    using System.Diagnostics;
    using System.Runtime.CompilerServices;
    using System.Linq.Expressions;

    public static class Global
    {
        public static int Gcd(params int[] nums)
        {
            var gcd = nums[0];
            for (var i = 1; i < nums.Length; i++)
                gcd = Gcd(nums[i], gcd);
            return gcd;
        }
        public static int Gcd(int a, int b) => b > a ? Gcd(b, a) : (b == 0 ? a : Gcd(b, a % b));
        public static int Lcm(int a, int b) => a / Gcd(a, b) * b;
        public static int Lcm(params int[] nums)
        {
            var lcm = nums[0];
            for (var i = 1; i < nums.Length; i++)
                lcm = Lcm(lcm, nums[i]);
            return lcm;
        }
        public static long Gcd(params long[] nums)
        {
            var gcd = nums[0];
            for (var i = 1; i < nums.Length; i++)
                gcd = Gcd(nums[i], gcd);
            return gcd;
        }
        public static long Gcd(long a, long b) => b > a ? Gcd(b, a) : (b == 0 ? a : Gcd(b, a % b));
        public static long Lcm(long a, long b) => a / Gcd(a, b) * b;

        public static long Lcm(params long[] nums)
        {
            var lcm = nums[0];
            for (var i = 1; i < nums.Length; i++)
                lcm = Lcm(lcm, nums[i]);
            return lcm;
        }

        public static T[] NewArray<T>(int len0, T value) => new T[len0].Fill(value);
        public static T[] NewArray<T>(int len0, Func<T> factory)
        {
            var arr = new T[len0];
            for (int i = 0; i < arr.Length; i++) arr[i] = factory();
            return arr;
        }
        public static T[][] NewArray<T>(int len0, int len1, T value) where T : struct
        {
            var arr = new T[len0][];
            for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, value);
            return arr;
        }
        public static T[][] NewArray<T>(int len0, int len1, Func<T> factory)
        {
            var arr = new T[len0][];
            for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, factory);
            return arr;
        }
        public static T[][][] NewArray<T>(int len0, int len1, int len2, T value) where T : struct
        {
            var arr = new T[len0][][];
            for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, value);
            return arr;
        }
        public static T[][][] NewArray<T>(int len0, int len1, int len2, Func<T> factory)
        {
            var arr = new T[len0][][];
            for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, factory);
            return arr;
        }
        public static T[][][][] NewArray<T>(int len0, int len1, int len2, int len3, T value) where T : struct
        {
            var arr = new T[len0][][][];
            for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, len3, value);
            return arr;
        }
        public static T[][][][] NewArray<T>(int len0, int len1, int len2, int len3, Func<T> factory)
        {
            var arr = new T[len0][][][];
            for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, len3, factory);
            return arr;
        }


        public static long Pow(long x, int y)
        {
            long res = 1;
            for (; y > 0; y >>= 1)
            {
                if ((y & 1) == 1) res *= x;
                x *= x;
            }
            return res;
        }
        public static BigInteger ParseBigInteger(ReadOnlySpan<char> s)
        {
            /* 自前実装の方が速い */
            if (s[0] == '-') return -ParseBigInteger(s[1..]);
            BigInteger res;
            if (s.Length % 9 == 0)
                res = 0;
            else
            {
                res = new BigInteger(int.Parse(s.Slice(0, s.Length % 9)));
                s = s.Slice(s.Length % 9);
            }

            while (s.Length > 0)
            {
                var sp = s.Slice(0, 9);
                res *= 1000_000_000;
                res += int.Parse(sp);
                s = s.Slice(9);
            }
            return res;
        }
        public static int PopCount(int x) => BitOperations.PopCount((uint)x);
        public static int PopCount(long x) => BitOperations.PopCount((ulong)x);
        public static int PopCount(ulong x) => BitOperations.PopCount(x);
        public static int MSB(int x) => BitOperations.Log2((uint)x);
        public static int MSB(uint x) => BitOperations.Log2(x);
        public static int MSB(long x) => BitOperations.Log2((ulong)x);
        public static int MSB(ulong x) => BitOperations.Log2(x);
        public static int LSB(int x) => BitOperations.TrailingZeroCount((uint)x);
        public static int LSB(uint x) => BitOperations.TrailingZeroCount(x);
        public static int LSB(long x) => BitOperations.TrailingZeroCount((ulong)x);
        public static int LSB(ulong x) => BitOperations.TrailingZeroCount(x);

    }
    public static class Ext
    {

        public static bool UpdateMax<T>(this ref T r, T val) where T : struct, IComparable<T>
        {
            if (r.CompareTo(val) < 0) { r = val; return true; }
            return false;
        }
        public static bool UpdateMin<T>(this ref T r, T val) where T : struct, IComparable<T>
        {
            if (r.CompareTo(val) > 0) { r = val; return true; }
            return false;
        }
        public static T[] Fill<T>(this T[] arr, T value)
        {
            Array.Fill(arr, value);
            return arr;
        }
        public static T[] Sort<T>(this T[] arr) { Array.Sort(arr); return arr; }
        public static string[] Sort(this string[] arr) => Sort(arr, StringComparer.Ordinal);
        public static T[] Sort<T, U>(this T[] arr, Expression<Func<T, U>> selector) where U : IComparable<U> => Sort(arr, ExComparer<T>.CreateExp(selector));
        public static T[] Sort<T>(this T[] arr, Comparison<T> comparison) { Array.Sort(arr, comparison); return arr; }
        public static T[] Sort<T>(this T[] arr, IComparer<T> comparer) { Array.Sort(arr, comparer); return arr; }
        public static T[] Reverse<T>(this T[] arr) { Array.Reverse(arr); return arr; }
        public static (int index, T max) MaxBy<T>(this T[] arr) where T : IComparable<T>
        {
            T max = arr[0];
            int maxIndex = 0;
            for (int i = 0; i < arr.Length; i++)
            {
                if (max.CompareTo(arr[i]) < 0)
                {
                    max = arr[i];
                    maxIndex = i;
                }
            }
            return (maxIndex, max);
        }
        public static (int index, T max) MaxBy<T, TMax>(this T[] arr, Func<T, TMax> maxBySelector) where TMax : IComparable<TMax>
        {
            var maxItem = maxBySelector(arr[0]);
            var max = arr[0];
            int maxIndex = 0;
            for (int i = 0; i < arr.Length; i++)
            {
                var nx = maxBySelector(arr[i]);
                if (maxItem.CompareTo(nx) < 0)
                {
                    maxItem = nx;
                    max = arr[i];
                    maxIndex = i;
                }
            }
            return (maxIndex, max);
        }
        public static (TSource item, TMax max) MaxBy<TSource, TMax>
            (this IEnumerable<TSource> source, Func<TSource, TMax> maxBySelector)
            where TMax : IComparable<TMax>
        {
            TMax max;
            TSource maxByItem;
            var e = source.GetEnumerator();
            e.MoveNext();
            maxByItem = e.Current;
            max = maxBySelector(maxByItem);
            while (e.MoveNext())
            {
                var item = e.Current;
                var next = maxBySelector(item);
                if (max.CompareTo(next) < 0)
                {
                    max = next;
                    maxByItem = item;
                }
            }
            return (maxByItem, max);
        }
        public static (int index, T min) MinBy<T>(this T[] arr) where T : IComparable<T>
        {
            T min = arr[0];
            int minIndex = 0;
            for (int i = 0; i < arr.Length; i++)
            {
                if (min.CompareTo(arr[i]) > 0)
                {
                    min = arr[i];
                    minIndex = i;
                }
            }
            return (minIndex, min);
        }
        public static (int index, T min) MinBy<T, TMin>(this T[] arr, Func<T, TMin> minBySelector) where TMin : IComparable<TMin>
        {
            var minItem = minBySelector(arr[0]);
            var min = arr[0];
            int minIndex = 0;
            for (int i = 0; i < arr.Length; i++)
            {
                var nx = minBySelector(arr[i]);
                if (minItem.CompareTo(nx) > 0)
                {
                    minItem = nx;
                    min = arr[i];
                    minIndex = i;
                }
            }
            return (minIndex, min);
        }
        public static (TSource item, TMin min) MinBy<TSource, TMin>
            (this IEnumerable<TSource> source, Func<TSource, TMin> minBySelector)
            where TMin : IComparable<TMin>
        {
            TMin min;
            TSource minByItem;

            var e = source.GetEnumerator();
            e.MoveNext();
            minByItem = e.Current;
            min = minBySelector(minByItem);
            while (e.MoveNext())
            {
                var item = e.Current;
                var next = minBySelector(item);
                if (min.CompareTo(next) > 0)
                {
                    min = next;
                    minByItem = item;
                }
            }
            return (minByItem, min);
        }
        public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count());
        public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i);
        public static Span<T> AsSpan<T>(this List<T> list, int start = 0) => Unsafe.As<Tuple<T[]>>(list).Item1.AsSpan(start, list.Count);
        public static ref T Get<T>(this T[] arr, int index)
        {
            if (index < 0)
                return ref arr[arr.Length + index];
            return ref arr[index];
        }
        public static TValue Get<TKey, TValue>(this IDictionary<TKey, TValue> dic, TKey key)
        {
            dic.TryGetValue(key, out var v);
            return v;
        }
    }
    public static class ExComparer<T>
    {
        class ExpressionComparer<K> : IComparer<T> where K : IComparable<K>
        {
            private class ParameterReplaceVisitor : ExpressionVisitor
            {
                private readonly ParameterExpression from;
                private readonly ParameterExpression to;
                public ParameterReplaceVisitor(ParameterExpression from, ParameterExpression to)
                {
                    this.from = from;
                    this.to = to;
                }
                protected override Expression VisitParameter(ParameterExpression node) => node == from ? to : base.VisitParameter(node);
            }

            readonly Comparison<T> func;
            public ExpressionComparer(Expression<Func<T, K>> expression)
            {
                var paramA = expression.Parameters[0];
                var paramB = Expression.Parameter(typeof(T));
                var f2 = (Expression<Func<T, K>>)new ParameterReplaceVisitor(expression.Parameters[0], paramB).Visit(expression);
                var compExp = Expression.Lambda<Comparison<T>>(Expression.Call(
                        expression.Body,
                        typeof(K).GetMethod(nameof(IComparable<K>.CompareTo), new[] { typeof(K) }),
                        f2.Body),
                        paramA, paramB);
                this.func = compExp.Compile();
            }
            public int Compare(T x, T y) => func(x, y);
            public override bool Equals(object obj) => obj is ExpressionComparer<K> c && this.func == c.func;
            public override int GetHashCode() => func.GetHashCode();
        }
        class ReverseComparer : IComparer<T>
        {
            private static Comparer<T> orig = Comparer<T>.Default;
            public int Compare(T y, T x) => orig.Compare(x, y);
            public override bool Equals(object obj) => obj is ReverseComparer;
            public override int GetHashCode() => GetType().GetHashCode();
        }
        public static IComparer<T> CreateExp<K>(Expression<Func<T, K>> expression) where K : IComparable<K> => new ExpressionComparer<K>(expression);
        public static readonly IComparer<T> DefaultReverse = new ReverseComparer();
    }
    public class ΔDebugView<T> { private IEnumerable<T> collection; public ΔDebugView(IEnumerable<T> collection) { this.collection = collection ?? throw new ArgumentNullException(nameof(collection)); }[DebuggerBrowsable(DebuggerBrowsableState.RootHidden)] public T[] Items => collection.ToArray(); }


    [DebuggerStepThrough]
    public class ConsoleReader
    {
        const int BufSize = 1 << 12;
        private readonly byte[] buffer = new byte[BufSize];
        private readonly Stream input;
        private readonly Encoding encoding;
        private int pos = 0;
        private int len = 0;
        public ConsoleReader(Stream input, Encoding encoding) { this.input = input; this.encoding = encoding; }
        public ConsoleReader() : this(Console.OpenStandardInput(), Console.InputEncoding) { }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        private void MoveNext() { if (++pos >= len) { len = input.Read(buffer, 0, buffer.Length); if (len == 0) { buffer[0] = 10; } pos = 0; } }

        public int Int
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get
            {
                int res = 0;
                bool neg = false;
                while (buffer[pos] < 48) { neg = buffer[pos] == 45; MoveNext(); }
                do { res = checked(res * 10 + (buffer[pos] ^ 48)); MoveNext(); } while (48 <= buffer[pos]);
                return neg ? -res : res;
            }
        }
        public int Int0 => this.Int - 1;
        public long Long
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get
            {
                long res = 0;
                bool neg = false;
                while (buffer[pos] < 48) { neg = buffer[pos] == 45; MoveNext(); }
                do { res = res * 10 + (buffer[pos] ^ 48); MoveNext(); } while (48 <= buffer[pos]);
                return neg ? -res : res;
            }
        }
        public long Long0 => this.Long - 1;
        public string String
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get
            {
                var sb = new List<byte>();
                while (buffer[pos] <= 32) MoveNext();
                do { sb.Add(buffer[pos]); MoveNext(); } while (32 < buffer[pos]);
                return this.encoding.GetString(sb.ToArray());
            }
        }
        public string Ascii
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get
            {
                var sb = new StringBuilder();
                while (buffer[pos] <= 32) MoveNext();
                do { sb.Append((char)buffer[pos]); MoveNext(); } while (32 < buffer[pos]);
                return sb.ToString();
            }
        }
        public string Line
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get
            {
                var sb = new List<byte>();
                while (buffer[pos] <= 32) MoveNext();
                do { sb.Add(buffer[pos]); MoveNext(); } while (buffer[pos] != 10 && buffer[pos] != 13);
                return this.encoding.GetString(sb.ToArray());
            }
        }
        public char Char
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get
            {
                while (buffer[pos] <= 32) MoveNext();
                char res = (char)buffer[pos];
                MoveNext();
                return res;
            }
        }
        public double Double => double.Parse(this.Ascii);

        [DebuggerStepThrough]
        public struct RepeatReader
        {
            ConsoleReader cr;
            int count;
            public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; }
            public T[] Select<T>(Func<ConsoleReader, T> factory) { var arr = new T[count]; for (var i = 0; i < count; i++) arr[i] = factory(cr); return arr; }
            public T[] Select<T>(Func<ConsoleReader, int, T> factory) { var arr = new T[count]; for (var i = 0; i < count; i++) arr[i] = factory(cr, i); return arr; }
            public string[] Line { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.Line; return arr; } }
            public string[] String { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.String; return arr; } }
            public string[] Ascii { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.Ascii; return arr; } }
            public int[] Int { get { var arr = new int[count]; for (var i = 0; i < count; i++) arr[i] = cr.Int; return arr; } }
            public int[] Int0 { get { var arr = new int[count]; for (var i = 0; i < count; i++) arr[i] = cr.Int0; return arr; } }
            public long[] Long { get { var arr = new long[count]; for (var i = 0; i < count; i++) arr[i] = cr.Long; return arr; } }
            public long[] Long0 { get { var arr = new long[count]; for (var i = 0; i < count; i++) arr[i] = cr.Long0; return arr; } }
            public double[] Double { get { var arr = new double[count]; for (var i = 0; i < count; i++) arr[i] = cr.Double; return arr; } }

            public static implicit operator int[](RepeatReader rr) => rr.Int;
            public static implicit operator long[](RepeatReader rr) => rr.Long;
            public static implicit operator double[](RepeatReader rr) => rr.Double;
            public static implicit operator string[](RepeatReader rr) => rr.Ascii;
        }
        public RepeatReader Repeat(int count) => new RepeatReader(this, count);

        [DebuggerStepThrough]
        public struct SplitReader
        {
            ConsoleReader cr;
            public SplitReader(ConsoleReader cr) { this.cr = cr; }
            public string[] String { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<string>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.String); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } }
            public string[] Ascii { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<string>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Ascii); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } }
            public int[] Int { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<int>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Int); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } }
            public int[] Int0 { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<int>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Int0); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } }
            public long[] Long { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<long>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Long); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } }
            public long[] Long0 { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<long>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Long0); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } }
            public double[] Double { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<double>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Double); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } }

            public static implicit operator int[](SplitReader sr) => sr.Int;
            public static implicit operator long[](SplitReader sr) => sr.Long;
            public static implicit operator double[](SplitReader sr) => sr.Double;
            public static implicit operator string[](SplitReader sr) => sr.Ascii;
        }
        public SplitReader Split => new SplitReader(this);

        public static implicit operator int(ConsoleReader cr) => cr.Int;
        public static implicit operator long(ConsoleReader cr) => cr.Long;
        public static implicit operator double(ConsoleReader cr) => cr.Double;
        public static implicit operator string(ConsoleReader cr) => cr.Ascii;
    }
    [DebuggerStepThrough]
    public class ConsoleWriter
    {
        [DebuggerBrowsable(DebuggerBrowsableState.Never)] public readonly StreamWriter sw;
        public ConsoleWriter() : this(Console.OpenStandardOutput(), Console.OutputEncoding) { }
        public ConsoleWriter(Stream output, Encoding encoding) { sw = new StreamWriter(output, encoding); }
        public void Flush() => sw.Flush();
        public ConsoleWriter WriteLine(ReadOnlySpan<char> obj) { sw.WriteLine(obj); return this; }
        public ConsoleWriter WriteLine<T>(T obj) { sw.WriteLine(obj.ToString()); return this; }
        public ConsoleWriter WriteLineJoin<T>(Span<T> col) => WriteMany(' ', (ReadOnlySpan<T>)col);
        public ConsoleWriter WriteLineJoin<T>(ReadOnlySpan<T> col) => WriteMany(' ', col);
        public ConsoleWriter WriteLineJoin<T>(IEnumerable<T> col) => WriteMany(' ', col);
        public ConsoleWriter WriteLineJoin<T>(params T[] col) => WriteMany(' ', col);
        public ConsoleWriter WriteLineJoin(params object[] col) => WriteMany(' ', col);
        public ConsoleWriter WriteLineJoin<T1, T2>(T1 v1, T2 v2)
        {
            sw.Write(v1.ToString()); sw.Write(' ');
            sw.WriteLine(v2.ToString()); return this;
        }
        public ConsoleWriter WriteLineJoin<T1, T2, T3>(T1 v1, T2 v2, T3 v3)
        {
            sw.Write(v1.ToString()); sw.Write(' ');
            sw.Write(v2.ToString()); sw.Write(' ');
            sw.WriteLine(v3.ToString()); return this;
        }
        public ConsoleWriter WriteLineJoin<T1, T2, T3, T4>(T1 v1, T2 v2, T3 v3, T4 v4)
        {
            sw.Write(v1.ToString()); sw.Write(' ');
            sw.Write(v2.ToString()); sw.Write(' ');
            sw.Write(v3.ToString()); sw.Write(' ');
            sw.WriteLine(v4.ToString()); return this;
        }
        public ConsoleWriter WriteLines<T>(Span<T> col) => WriteMany('\n', (ReadOnlySpan<T>)col);
        public ConsoleWriter WriteLines<T>(ReadOnlySpan<T> col) => WriteMany('\n', col);
        public ConsoleWriter WriteLines<T>(IEnumerable<T> col) => WriteMany('\n', col);
        public ConsoleWriter WriteLineGrid<T>(IEnumerable<IEnumerable<T>> cols)
        {
            foreach (var col in cols)
                WriteLineJoin(col);
            return this;
        }
        private ConsoleWriter WriteMany<T>(char sep, ReadOnlySpan<T> col)
        {
            var en = col.GetEnumerator();
            if (!en.MoveNext())
                return this;
            sw.Write(en.Current.ToString());
            while (en.MoveNext())
            {
                sw.Write(sep);
                sw.Write(en.Current.ToString());
            }
            sw.WriteLine();
            return this;
        }
        private ConsoleWriter WriteMany<T>(char sep, IEnumerable<T> col)
        {
            var en = col.GetEnumerator();
            if (!en.MoveNext())
                return this;
            sw.Write(en.Current.ToString());
            while (en.MoveNext())
            {
                sw.Write(sep);
                sw.Write(en.Current.ToString());
            }
            sw.WriteLine();
            return this;
        }
    }
}
public partial class Program
{
    [System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] public ConsoleReader cr;
    [System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] public ConsoleWriter cw;
    public Program(ConsoleReader reader, ConsoleWriter writer) { this.cr = reader; this.cw = writer; System.Globalization.CultureInfo.CurrentCulture = System.Globalization.CultureInfo.InvariantCulture; }
    static void Main() => new Program(new ConsoleReader(), new ConsoleWriter()).Run();
    public void Run()
    {
        var res = Calc();
        if (res is double)
            cw.WriteLine(Result((double)res));
        else if (res is bool)
            cw.WriteLine(Result((bool)res));
        else if (res != null)
            cw.WriteLine(res.ToString());
        cw.Flush();
    }
}
public partial class Program
{
    public static string Result(double d) => d.ToString("0.####################", System.Globalization.CultureInfo.InvariantCulture);
    #endregion
    public static string Result(bool b) => b ? "Yes" : "No";
    private object Calc()
    {
        n = cr;
        m = cr;
        graph = new WGraphBuilder(n, cr, m, false).ToArray();
        status = NewArray(n, new St());
        status[0] = new St { even = 0 };
        try
        {
            CalcImpl();
            long max = long.MaxValue;
            long min = 1;
            long? f = null;
            foreach (var st in status)
            {
                if (st.even is { } e)
                {
                    min.UpdateMax(1 - e);
                    if (st.odd is { } o)
                    {
                        var ff = o - e;
                        if (ff % 2 == 1) return 0;
                        ff >>= 1;
                        if (f.HasValue && f != ff) return 0;
                        f = ff;
                    }
                }
                else if (st.odd is { } o) max.UpdateMin(o - 1);
            }
            if (f is { } fff)
                return min <= fff && fff <= max ? 1 : 0;
            return Math.Max(0, max - min + 1);
        }
        catch
        {
            return 0;
        }
    }
    void CalcImpl()
    {
        var queue = new Queue<int>(n);
        queue.Enqueue(0);
        while (queue.Count > 0)
        {
            int v = queue.Dequeue();
            var cur = status[v];
            foreach (var next in graph[v].children)
            {
                if (!sumi.Add(N(v, next.to))) continue;
                queue.Enqueue(next.to);
                ref var st = ref status[next.to];
                if (cur.even is { } e)
                {
                    if (st.odd.HasValue && st.odd != next.value - e) { Console.WriteLine(0); Environment.Exit(0); }
                    st.odd = next.value - e;
                }
                if (cur.odd is { } o)
                {
                    if (st.even.HasValue && st.even != next.value - o) { Console.WriteLine(0); Environment.Exit(0); }
                    st.even = next.value - o;
                }
            }
        }
    }
    (int, int) N(int s, int t) => s < t ? (s, t) : (t, s);
    HashSet<(int, int)> sumi = new HashSet<(int, int)>((int)5e6);
    St[] status;
    WNode[] graph;
    int n;
    int m;
}

class WGraphBuilder { private List<Next>[] roots; private List<Next>[] children; public WGraphBuilder(int count, bool isOriented) { this.roots = new List<Next>[count]; this.children = new List<Next>[count]; for (var i = 0; i < count; i++) { if (isOriented) { this.roots[i] = new List<Next>(); this.children[i] = new List<Next>(); } else { this.roots[i] = this.children[i] = new List<Next>(); } } } public WGraphBuilder(int count, ConsoleReader cr, int edgeCount, bool isOriented) : this(count, isOriented) { for (var i = 0; i < edgeCount; i++) this.Add(cr.Int0, cr.Int0, cr.Int); } public void Add(int from, int to, int value) { children[from].Add(new Next { to = to, value = value }); roots[to].Add(new Next { to = from, value = value }); } public WNode[] ToArray() => Enumerable.Zip(roots, children, (root, child) => (root, child)).Select((t, i) => new WNode(i, t.root.ToArray(), t.child.ToArray())).ToArray(); public WTreeNode[] ToTree(int root) { if (this.roots[0] != this.children[0]) throw new Exception("木には無向グラフをしたほうが良い"); var res = new WTreeNode[this.children.Length]; res[root] = new WTreeNode(root, -1, 0, 0, this.children[root].ToArray()); var queue = new Queue<int>(); foreach (var child in res[root].children) { res[child.to] = new WTreeNode(child.to, root, 1, child.value, Array.Empty<Next>()); queue.Enqueue(child.to); } while (queue.Count > 0) { var from = queue.Dequeue(); if (res[from].root == -1) res[from].children = this.children[from].ToArray(); else { var children = new List<Next>(this.children[from].Count); foreach (var c in this.children[from]) if (c.to != res[from].root) children.Add(c); res[from].children = children.ToArray(); } foreach (var child in res[from].children) { res[child.to] = new WTreeNode(child.to, from, res[from].depth + 1, res[from].depthLength + child.value, Array.Empty<Next>()); queue.Enqueue(child.to); } } return res; } public WGraphBuilder Clone() { var count = this.roots.Length; var isOriented = this.roots[0] != this.children[0]; var cl = new WGraphBuilder(count, isOriented); for (int i = 0; i < count; i++) { if (isOriented) { cl.children[i] = this.children[i].ToList(); cl.roots[i] = this.roots[i].ToList(); } else cl.children[i] = cl.roots[i] = this.roots[i].ToList(); } return cl; } }
struct Next { public int to; public int value; public override string ToString() => $"to: {to} value:{value}"; }
class WTreeNode { public WTreeNode(int i, int root, int depth, long depthLength, Next[] children) { this.index = i; this.root = root; this.children = children; this.depth = depth; this.depthLength = depthLength; } public readonly int index; public readonly int root; public readonly int depth; public readonly long depthLength; public Next[] children; public override string ToString() => $"children: {string.Join(",", children)}"; public override bool Equals(object obj) { if (obj is WTreeNode) return this.Equals((WTreeNode)obj); else return false; } public bool Equals(WTreeNode other) => this.index == other.index; public override int GetHashCode() => this.index; }
class WNode { public WNode(int i, Next[] roots, Next[] children) { this.index = i; this.roots = roots; this.children = children; } public int index; public Next[] roots; public Next[] children; public override bool Equals(object obj) { if (obj is WNode) return this.Equals((WNode)obj); else return false; } public bool Equals(WNode other) => this.index == other.index; public override int GetHashCode() => this.index; public override string ToString() => $"children: ({string.Join("),(", children)})"; }
struct St
{
    public long? odd;
    public long? even;
    public override string ToString()
    {
        return $"o:{odd} e:{even}";
    }
}