This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#pragma GCC optimize ("O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,avx,avx2")
using namespace std;
typedef long long ll;
typedef __int128 lll;
typedef long double ld;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pld;
#define MAX 9223372036854775807LL
#define MIN -9223372036854775807LL
#define INF 0x3f3f3f3f3f3f3f3f
#define fi first
#define se second
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cout << fixed; cout.precision(10);
#define sp << " "
#define en << "\n"
#define compress(v) sort(v.begin(), v.end()), v.erase(unique(v.begin(), v.end()), v.end())
inline int readChar();
template<class T = int> inline T readInt();
template<class T> inline void writeInt(T x, char end = 0);
inline void writeChar(int x);
inline void writeWord(const char *s);
static const int buf_size = 1 << 18;
inline int getChar(){
static char buf[buf_size];
static int len = 0, pos = 0;
if(pos == len) pos = 0, len = fread(buf, 1, buf_size, stdin);
if(pos == len) return -1;
return buf[pos++];
}
inline int readChar(){
int c = getChar();
while(c <= 32) c = getChar();
return c;
}
template <class T>
inline T readInt(){
int s = 1, c = readChar();
T x = 0;
if(c == '-') s = -1, c = getChar();
while('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
return s == 1 ? x : -x;
}
static int write_pos = 0;
static char write_buf[buf_size];
inline void writeChar(int x){
if(write_pos == buf_size) fwrite(write_buf, 1, buf_size, stdout), write_pos = 0;
write_buf[write_pos++] = x;
}
template <class T>
inline void writeInt(T x, char end){
if(x < 0) writeChar('-'), x = -x;
char s[24]; int n = 0;
while(x || !n) s[n++] = '0' + x % 10, x /= 10;
while(n--) writeChar(s[n]);
if(end) writeChar(end);
}
inline void writeWord(const char *s){
while(*s) writeChar(*s++);
}
struct Flusher{
~Flusher(){ if(write_pos) fwrite(write_buf, 1, write_pos, stdout), write_pos = 0; }
}flusher;
int n, m;
int ss = 1000000007;
int ans;
int cou[2010];
int dp[9000010];
int fac[5010] = 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inv[5010] = 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5,948999635,226411351,932606953,648400853,982129316,222499192,210099381,364489884,900356301,452929681,389876919,923251661,107493176,324172060,905857720,397330109,485633214,900642399,409637722,706294847,901349710,219792632,733713110,896389937,380055091,346432996,2900598,665359562,182870654,884645068,180309339,412984412,417971731,218080016,206214849,989151633,389988583,307822805,949513229,847471937,310485194,203325095,933631970,960639971,825841,257947806,209160288,93703780,976064009,118099183,933477617,920360106,198140931,508402380,477192883,346906897,32901559,24745109,424291402,642895641,724699504,489929126,572714389,553155585,51471056,230186211,551214361,512625063,893741382,591383312,876098423,724218194,837454813,910303674,698177129,907549281,745896480,56590906,919054052,382574327,953433471,317491287,873121036,988099654,407996720,578711531,911380958,493635996,946126663,628635301,490947025,799969980,119130188,630742748,476377099,982254236,464663807,783800078,532504483,255915525,575736317,164628155,964909320,145160514,980286745,914969915,130494920,318018230,194112914,328272362,722905585,66189186,333442704,540321143,948437851,685981525,665760459,850646742,517313654,26917299,779029483,750349276,714646565,335620812,503229368,676623908,942644300,228174114,497200378,628473356,700252926,99863904,594636504,892377425,360787044,272132969,970430285,301786416,273525902,243009112,746873955,162342987,738300940,561546774,694317928,167849789,665356080,520787790,130528813,764534024,589478339,860127167,288345555,158442975,105590919,744346756,232010915,319424559,629445645,125845797,487740032,913151746,180640874,840761518,547055540,63828132,617497665,242075918,756064194,835244228,225501280,129371095,548109180,956528846,841980229,435371903,815828731,480854180,658370764,652865158,595983037,868241807,853308693,48832790,632227879,599471885,494928759,815315169,641409314,409823437,580383232,525343086,53716942,493854775,838150971,26723274,939798434,137223061,9130041,592783194,499757497,634820891,398780345,171313778,637161904,369630852,171435718,796737315,337902573,949690114,428938870,99794494,925952523,68174202,921189933,536187754,44060737,586227801,835750532,575754193,772554048,566393559,349074250,501155443,127888754,390368534,730923915,134748123,859149581,943729224,304943977,819009800,983519490,963694633,174030119,923510078,46048057,739292236,620730169,797254167,632847731,252150411,900145962,220639575,578658033,840881849,782899631,734895174,186258881,637780020,971415934,784538881,633215016,752934432,358301171,568850979,998569628,338862185,721331635,893610883,504049888,961731740,599516631,568769593,18809138,805575100,150198471,419944908,382100277,183564857,583359638,371086928,660731997,194457456,210273778,851732258,626893306,517188818,265388111,158969998,981460088,509414305,641252794,475586105,930843297,134848627,189739967,285054793,580121460,112423009,255576202,353406990,949479111,936867372,938705839,661089344,849012539,225077910,712483745,860862632,176740658,16703993,94201589,925362702,25988391,900942801,729373788,662351713,839870713,517361009,985592674,713132298,420117608,776964229,73612702,364645649,772456486,72776687,68430365,643800116,625393374,254952201,322872110,208675693,160726696,748101590,529802978,122680922,193621785,306251584,597340808,853460063,460070610,268058874,230520791,439429962,791704785,161885433,327961303,59620609,721221242,135167755,837274064,793212486,941516921,887787324,726752716,365413262,416396355,469258717,16568815,930888128,852024380,23844896,119903427,577802854,332968389,822815031,887874542,511509715,820433615,402311749,786677513,988162578,264273539,162638064,500681508,742195676,529481251,689905243,645791338,622353223,769900939,670866101,809111338,847499779,466134162,49123567,315143948,264366110,473416062,643159978,207658212,33692064,368925784,970037940,839055274,90335809,136698992,263139111,900601161,292446747,247213947,861527005,80269766,558455357,832755519,164000193,32791064,169551471,667386341,228226127,531886442,657842775,129444321,114832602,328379742,588229077,372648326,653765232,413225456,983910236,687322016,126628054,715076270,781272775,271867900,400776119,701035816,573914407,128900257,424817999,813632309,733050871,777486273,315627205,136958818,996506297,179137443,546896512,932396606,52097784,874667033,315519546,999324666,483651745,635776633,290003968,716584575,938622264,238366900,982480762,887015442,317993731,945374660,536112742,253959398,988529084,16793314,713788675,85871659,70913295,707004992,889511024,869559333,413881274,510236151,942348740,200285660,655050076};
int C[5010][5010];
void init(void)
{
C[0][0] = 1;
for(ll i = 1 ; i <= 2000 ; ++i)
{
C[i][0] = C[i][i] = 1;
for(ll j = 1 ; j < i ; ++j)
{
C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
if(C[i][j] > ss)
C[i][j] -= ss;
}
}
}
int main(void)
{
fastio
//cin >> n >> m;
n = readInt();
m = readInt();
init();
int siz = (n << 1);
ans = fac[siz];
for(int i = siz ; i >= 1 ; --i)
{
int gap = i % m;
if(gap == 0)
gap = m;
cou[gap]++;
}
for(int i = m ; i >= 0 ; --i)
dp[i] = 1;
for(int i = 1 ; i <= n ; ++i)
{
for(int j = 1 ; j <= m ; ++j)
{
int X = cou[j];
for(int k = 1 ; (k << 1) <= X && k <= i ; ++k)
{
int num = i * (m + 1) + j;
dp[num] = (dp[i * (m + 1) + j] + (ll)dp[(i - k) * (m + 1) + j - 1] * fac[X] % ss * inv[X - (k << 1)] % ss * C[i][k]% ss);
while(abs(dp[num]) > ss)
{
if(dp[num] < 0)
dp[num] += ss;
else
dp[num] -= ss;
}
}
}
for(int j = 1 ; j <= m ; ++j)
{
int num = i * (m + 1) + j;
dp[num] = (dp[num] + dp[num - 1]);
while(abs(dp[num]) > ss)
{
if(dp[num] < 0)
dp[num] += ss;
else
dp[num] -= ss;
}
}
}
for(int i = n ; i >= 1 ; --i)
{
int num = i * (m + 1) + m;
int gap = (ll)dp[num] * C[n][i] % ss * fac[(n - i) << 1] % ss;
if(i & 1)
ans = (ans - gap);
else
ans = (ans + gap);
while(abs(ans) > ss)
{
if(ans < 0)
ans += ss;
else
ans -= ss;
}
}
ans = (ans + ss) % ss;
writeInt(ans);
Flusher();
return 0;
}
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