Buggy python submission (verdict: Runtime Error):
# coding:utf-8
class Tree(object):
    def __init__(self, N):
        self.tree   = [[] for _ in range(N)]
        self.colors = [0  for _ in range(N)]

    def add_node(self, a, b):
        self.tree[a].append(b)
    # 二部グラフか判定する関数
    def is_bipartite_graph(self, v, color):
        self.colors[v] = color
        for to in self.tree[v]:
            if self.colors[to] == color:
                return False
            if self.colors[to] == 0:
                self.is_bipartite_graph(to, -color)
        return True
    
    def count_node(self, color):
        return self.colors.count(color)
    
if __name__ == "__main__":

    # input data
    N, M = map(int, input().split())
    tree = Tree(N)
    for _ in range(M):
        a, b = map(int, input().split())
        tree.add_node(a-1, b-1)
        tree.add_node(b-1, a-1)
    
    # tree dp
    is_bpr = tree.is_bipartite_graph(0, 1)
    if is_bpr:
        bla = tree.count_node(1)
        whi = N - bla
        print(bla*whi-M)
    else:
        print(int(N*(N-1)/2-M))



Fixed submission:
# coding:utf-8
class Tree(object):
    def __init__(self, N):
        self.tree   = [[] for _ in range(N)]
        self.colors = [0  for _ in range(N)]

    def add_node(self, a, b):
        self.tree[a].append(b)
    # 二部グラフか判定する関数
    def is_bipartite_graph(self, v, color):
        self.colors[v] = color
        for to in self.tree[v]:
            if self.colors[to] == color:
                return False
            if self.colors[to] == 0 and not self.is_bipartite_graph(to, -color):
                return False
        return True
    
    def count_node(self, color):
        return self.colors.count(color)
    
if __name__ == "__main__":

    import sys
    sys.setrecursionlimit(200000)
    # input data
    N, M = map(int, input().split())
    tree = Tree(N)
    for _ in range(M):
        a, b = map(int, input().split())
        tree.add_node(a-1, b-1)
        tree.add_node(b-1, a-1)
    
    # tree dp
    is_bpr = tree.is_bipartite_graph(0, 1)
    if is_bpr:
        bla = tree.count_node(1)
        whi = N - bla
        print(bla*whi-M)
    else:
        print(int(N*(N-1)/2-M))

Buggy python submission (verdict: Runtime Error):
# coding:utf-8
class Tree(object):
    def __init__(self, N):
        self.tree   = [[] for _ in range(N)]
        self.colors = [0  for _ in range(N)]

    def add_node(self, a, b):
        self.tree[a].append(b)
    # 二部グラフか判定する関数
    def is_bipartite_graph(self, v, color):
        self.colors[v] = color
        for to in self.tree[v]:
            if self.colors[to] == color:
                return False
            if self.colors[to] == 0 and not self.is_bipartite_graph(to, -color):
                return False
        return True
    
    def count_node(self, color):
        return self.colors.count(color)
    
if __name__ == "__main__":

    # input data
    N, M = map(int, input().split())
    tree = Tree(N)
    for _ in range(M):
        a, b = map(int, input().split())
        tree.add_node(a-1, b-1)
        tree.add_node(b-1, a-1)
    
    # tree dp
    is_bpr = tree.is_bipartite_graph(0, 1)
    if is_bpr:
        bla = tree.count_node(1)
        whi = N - bla
        print(bla*whi-M)
    else:
        print(int(N*(N-1)/2-M))



Fixed submission:
# coding:utf-8
class Tree(object):
    def __init__(self, N):
        self.tree   = [[] for _ in range(N)]
        self.colors = [0  for _ in range(N)]

    def add_node(self, a, b):
        self.tree[a].append(b)
    # 二部グラフか判定する関数
    def is_bipartite_graph(self, v, color):
        self.colors[v] = color
        for to in self.tree[v]:
            if self.colors[to] == color:
                return False
            if self.colors[to] == 0 and not self.is_bipartite_graph(to, -color):
                return False
        return True
    
    def count_node(self, color):
        return self.colors.count(color)
    
if __name__ == "__main__":

    import sys
    sys.setrecursionlimit(200000)
    # input data
    N, M = map(int, input().split())
    tree = Tree(N)
    for _ in range(M):
        a, b = map(int, input().split())
        tree.add_node(a-1, b-1)
        tree.add_node(b-1, a-1)
    
    # tree dp
    is_bpr = tree.is_bipartite_graph(0, 1)
    if is_bpr:
        bla = tree.count_node(1)
        whi = N - bla
        print(bla*whi-M)
    else:
        print(int(N*(N-1)/2-M))

Buggy python submission (verdict: Runtime Error):
# coding:utf-8
class Tree(object):
    def __init__(self, N):
        self.tree   = [[] for _ in range(N)]
        self.colors = [0  for _ in range(N)]

    def add_node(self, a, b):
        self.tree[a].append(b)
    # 二部グラフか判定する関数
    def is_bipartite_graph(self, v, color):
        self.colors[v] = color
        for to in self.tree[v]:
            if self.colors[to] == color:
                return False
            if self.colors[to] == 0 and not self.is_bipartite_graph(to, -color):
                return False
        return True
    
    def count_node(self, color):
        return self.colors.count(color)
    
if __name__ == "__main__":

    # input data
    N, M = map(int, input().split())
    tree = Tree(N)
    for _ in range(M):
        a, b = map(int, input().split())
        tree.add_node(a-1, b-1)
        tree.add_node(b-1, a-1)
    
    # tree dp
    is_bpr = tree.is_bipartite_graph(0, 1)
    if is_bpr:
        bla = tree.count_node(1)
        whi = N - bla
        print(bla*whi-M)
    else:
        print(N*(N-1)/2-M)



Fixed submission:
# coding:utf-8
class Tree(object):
    def __init__(self, N):
        self.tree   = [[] for _ in range(N)]
        self.colors = [0  for _ in range(N)]

    def add_node(self, a, b):
        self.tree[a].append(b)
    # 二部グラフか判定する関数
    def is_bipartite_graph(self, v, color):
        self.colors[v] = color
        for to in self.tree[v]:
            if self.colors[to] == color:
                return False
            if self.colors[to] == 0 and not self.is_bipartite_graph(to, -color):
                return False
        return True
    
    def count_node(self, color):
        return self.colors.count(color)
    
if __name__ == "__main__":

    import sys
    sys.setrecursionlimit(200000)
    # input data
    N, M = map(int, input().split())
    tree = Tree(N)
    for _ in range(M):
        a, b = map(int, input().split())
        tree.add_node(a-1, b-1)
        tree.add_node(b-1, a-1)
    
    # tree dp
    is_bpr = tree.is_bipartite_graph(0, 1)
    if is_bpr:
        bla = tree.count_node(1)
        whi = N - bla
        print(bla*whi-M)
    else:
        print(int(N*(N-1)/2-M))