Buggy python submission (verdict: Time Limit Exceeded):
#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#

"""
AGC028 D
"""

import itertools
from functools import reduce
from functools import lru_cache

nn, k = map(int, input().split())
n = 2*nn
abli = []
for i in range(k):
    a, b = map(int, input().split())
    if a < b:
        abli.append((a, b))
    else:
        abli.append((b, a))
flattenabli = itertools.chain.from_iterable(abli)

cut = 10**9+7

unused = [1 for i in range(n+1)]
for a in flattenabli:
    unused[a] -= 1
unusedacum = list(itertools.accumulate(unused))


def modInverse(a, b, divmod=divmod):
    r0, r1, s0, s1 = a, b, 1, 0
    while r1 != 0:
        q, rtmp = divmod(r0, r1)
        stmp = s0-q*s1
        r0, s0 = r1, s1
        r1, s1 = rtmp, stmp
    return s0 % cut


@lru_cache(maxsize=None)
def doubleFactorial(x):
    return reduce(lambda y, z: y*z % cut, range(x, 0, -2))


@lru_cache(maxsize=None)
def isSandwiched(i, j):
    return any(map(lambda k: abli[k][0] < i <= abli[k][1] <= j or i <= abli[k][0] <= j < abli[k][1], range(k)))


nonSandwichedNums = [[] for i in range(n+1)]
for i in range(1, n+1):
    for j in range(i+1, n+1):
        if not isSandwiched(i, j):
            nonSandwichedNums[i].append(j)


def numberUnderterminedBetween(i, j):
    return unusedacum[j]-unusedacum[i-1]


def pairCombinations(x):
    if x == 0:
        return 1
    elif x % 2 == 0:
        return doubleFactorial(x-1)
    else:
        return 0


def g(i, j):
    x = numberUnderterminedBetween(i, j)
    return pairCombinations(x)


undetermined = numberUnderterminedBetween(1, n)

ggg = [[0]*(i+1) for i in range(n+1)]
for i in range(1, n+1):
    for j in range(i+1, n+1):
        ggg[i].append(g(i, j))

ans = 0
dp = [[0]*(n+1) for i in range(n+1)]
for i in range(1, n+1):
    for j in nonSandwichedNums[i]:
        dp[i][j] = (ggg[i][j]-sum([dp[i][kk]*ggg[kk+1][j] for kk in nonSandwichedNums[i] if kk < j])) % cut
        ans = (ans + dp[i][j]*pairCombinations(undetermined-numberUnderterminedBetween(i, j))) % cut


print(ans)


Fixed submission:
#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#

"""
AGC028 D
"""

import itertools
from functools import reduce
from functools import lru_cache

nn, k = map(int, input().split())
n = 2*nn
abli = []
for i in range(k):
    a, b = map(int, input().split())
    if a < b:
        abli.append((a, b))
    else:
        abli.append((b, a))
flattenabli = itertools.chain.from_iterable(abli)

cut = 10**9+7

unused = [1 for i in range(n+1)]
for a in flattenabli:
    unused[a] -= 1
unusedacum = list(itertools.accumulate(unused))


def modInverse(a, b, divmod=divmod):
    r0, r1, s0, s1 = a, b, 1, 0
    while r1 != 0:
        q, rtmp = divmod(r0, r1)
        stmp = s0-q*s1
        r0, s0 = r1, s1
        r1, s1 = rtmp, stmp
    return s0 % cut


@lru_cache(maxsize=None)
def doubleFactorial(x):
    return reduce(lambda y, z: y*z % cut, range(x, 0, -2))


@lru_cache(maxsize=None)
def isSandwiched(i, j):
    return any(map(lambda k: abli[k][0] < i <= abli[k][1] <= j or i <= abli[k][0] <= j < abli[k][1], range(k)))


nonSandwichedNums = [[] for i in range(n+1)]
for i in range(1, n+1):
    for j in range(i+1, n+1):
        if not isSandwiched(i, j):
            nonSandwichedNums[i].append(j)


def numberUnderterminedBetween(i, j):
    return unusedacum[j]-unusedacum[i-1]


def pairCombinations(x):
    if x == 0:
        return 1
    elif x % 2 == 0:
        return doubleFactorial(x-1)
    else:
        return 0


def g(i, j):
    x = numberUnderterminedBetween(i, j)
    return pairCombinations(x)


undetermined = numberUnderterminedBetween(1, n)

ggg = [[0]*(i+1) for i in range(n+1)]
for i in range(1, n+1):
    for j in range(i+1, n+1):
        ggg[i].append(g(i, j))

ans = 0
dp = [[0]*(n+1) for i in range(n+1)]
for i in range(1, n+1):
    for j in nonSandwichedNums[i]:
        gg = ggg[i][j]
        if gg != 0:
            dp[i][j] = (ggg[i][j]-sum([dp[i][kk]*ggg[kk+1][j] for kk in nonSandwichedNums[i] if kk < j])) % cut
        else:
            dp[i][j] = 0
        ans = (ans + dp[i][j]*pairCombinations(undetermined-numberUnderterminedBetween(i, j))) % cut


print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#

"""
AGC028 D
"""

import itertools
from functools import reduce
from functools import lru_cache

nn, k = map(int, input().split())
n = 2*nn
abli = []
for i in range(k):
    a, b = map(int, input().split())
    if a < b:
        abli.append((a, b))
    else:
        abli.append((b, a))
flattenabli = itertools.chain.from_iterable(abli)

cut = 10**9+7

unused = [1 for i in range(n+1)]
for a in flattenabli:
    unused[a] -= 1
unusedacum = list(itertools.accumulate(unused))


def modInverse(a, b, divmod=divmod):
    r0, r1, s0, s1 = a, b, 1, 0
    while r1 != 0:
        q, rtmp = divmod(r0, r1)
        stmp = s0-q*s1
        r0, s0 = r1, s1
        r1, s1 = rtmp, stmp
    return s0 % cut


@lru_cache(maxsize=None)
def doubleFactorial(x):
    return reduce(lambda y, z: y*z % cut, range(x, 0, -2))


@lru_cache(maxsize=None)
def isSandwiched(i, j):
    return any(map(lambda k: abli[k][0] < i <= abli[k][1] <= j or i <= abli[k][0] <= j < abli[k][1], range(k)))


nonSandwichedNums = [[] for i in range(n+1)]
for i in range(1, n+1):
    for j in range(i+1, n+1):
        if not isSandwiched(i, j):
            nonSandwichedNums[i].append(j)


def numberUnderterminedBetween(i, j):
    return unusedacum[j]-unusedacum[i-1]


def pairCombinations(x):
    if x == 0:
        return 1
    elif x % 2 == 0:
        return doubleFactorial(x-1)
    else:
        return 0


def g(i, j):
    x = numberUnderterminedBetween(i, j)
    return pairCombinations(x)


undetermined = numberUnderterminedBetween(1, n)

ggg = [[0]*(i+1) for i in range(n+1)]
for i in range(1, n+1):
    for j in range(i+1, n+1):
        ggg[i].append(g(i, j))



@lru_cache(maxsize=None)
def dp(i, j):
    if isSandwiched(i, j):
        return 0
    gg = ggg[i][j]
    if gg == 0:
        return 0
    # return gg-sum([dp(i, k)*g(k+1, j) for k in range(i+1, j)]) % cut
    return (gg-sum([dp(i, k)*ggg[k+1][j] for k in nonSandwichedNums[i] if k < j])) % cut


print(sum([dp(i, j)*pairCombinations(undetermined-numberUnderterminedBetween(i, j)) for i, j in itertools.combinations(range(1, n+1), 2)]) % cut)


Fixed submission:
#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#

"""
AGC028 D
"""

import itertools
from functools import reduce
from functools import lru_cache

nn, k = map(int, input().split())
n = 2*nn
abli = []
for i in range(k):
    a, b = map(int, input().split())
    if a < b:
        abli.append((a, b))
    else:
        abli.append((b, a))
flattenabli = itertools.chain.from_iterable(abli)

cut = 10**9+7

unused = [1 for i in range(n+1)]
for a in flattenabli:
    unused[a] -= 1
unusedacum = list(itertools.accumulate(unused))


def modInverse(a, b, divmod=divmod):
    r0, r1, s0, s1 = a, b, 1, 0
    while r1 != 0:
        q, rtmp = divmod(r0, r1)
        stmp = s0-q*s1
        r0, s0 = r1, s1
        r1, s1 = rtmp, stmp
    return s0 % cut


@lru_cache(maxsize=None)
def doubleFactorial(x):
    return reduce(lambda y, z: y*z % cut, range(x, 0, -2))


@lru_cache(maxsize=None)
def isSandwiched(i, j):
    return any(map(lambda k: abli[k][0] < i <= abli[k][1] <= j or i <= abli[k][0] <= j < abli[k][1], range(k)))


nonSandwichedNums = [[] for i in range(n+1)]
for i in range(1, n+1):
    for j in range(i+1, n+1):
        if not isSandwiched(i, j):
            nonSandwichedNums[i].append(j)


def numberUnderterminedBetween(i, j):
    return unusedacum[j]-unusedacum[i-1]


def pairCombinations(x):
    if x == 0:
        return 1
    elif x % 2 == 0:
        return doubleFactorial(x-1)
    else:
        return 0


def g(i, j):
    x = numberUnderterminedBetween(i, j)
    return pairCombinations(x)


undetermined = numberUnderterminedBetween(1, n)

ggg = [[0]*(i+1) for i in range(n+1)]
for i in range(1, n+1):
    for j in range(i+1, n+1):
        ggg[i].append(g(i, j))

ans = 0
dp = [[0]*(n+1) for i in range(n+1)]
for i in range(1, n+1):
    for j in nonSandwichedNums[i]:
        gg = ggg[i][j]
        if gg != 0:
            dp[i][j] = (ggg[i][j]-sum([dp[i][kk]*ggg[kk+1][j] for kk in nonSandwichedNums[i] if kk < j])) % cut
        else:
            dp[i][j] = 0
        ans = (ans + dp[i][j]*pairCombinations(undetermined-numberUnderterminedBetween(i, j))) % cut


print(ans)