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ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#211284 | #3082. Ascending Matrix | zhouhuanyi | AC ✓ | 330ms | 46916kb | C++14 | 2.6kb | 2023-10-12 14:12:22 | 2023-10-12 14:12:23 |
Judging History
answer
#include<iostream>
#include<cstdio>
#define int long long
#define mod 998244353
#define N 2000
using namespace std;
int read()
{
char c=0;
int sum=0;
while (c<'0'||c>'9') c=getchar();
while ('0'<=c&&c<='9') sum=sum*10+c-'0',c=getchar();
return sum;
}
int n,m,k,s[N+1][N+1],s1[N+1][N+1],s2[N+1][N+1],C[N+1][N+1],A[N+1],S[N+1],T[N+1],inv[N+1];
long long fast_pow(long long a,int b)
{
if (b==0) return 1;
if (b&1) return fast_pow(a*a%mod,b/2)*a%mod;
else return fast_pow(a*a%mod,b/2);
}
int F(int x1,int y1,int x2,int y2)
{
if (x1<x2) return 0;
if (y1>y2) return 0;
return C[x1-x2+y2-y1][x1-x2];
}
int G(int x1,int y1,int x2,int y2,int X,int Y)
{
if (x1<x2) return 0;
if (y1>y2) return 0;
if (Y>=y2) return F(x1,y1,x2,y2);
long long res=0;
for (int i=x2;i<=X;++i) res=(res+F(x1,y1,i,Y)*F(i,Y+1,x2,y2)%mod)%mod;
return res;
}
int gauss(int x)
{
long long st,res=1;
for (int i=1;i<=k;++i)
for (int j=1;j<=k;++j)
s[i][j]=(s1[i][j]*x%mod+s2[i][j])%mod;
for (int i=1;i<=k;++i)
{
for (int j=i+1;j<=k;++j)
if (!s[i][i]&&s[j][i])
swap(s[i],s[j]),res=-res;
if (s[i][i])
{
for (int j=i+1;j<=k;++j)
{
st=s[j][i]*fast_pow(s[i][i],mod-2)%mod;
for (int t=i;t<=k;++t) s[j][t]=(s[j][t]-s[i][t]*st%mod)%mod;
}
}
}
for (int i=1;i<=k;++i) res=res*s[i][i]%mod;
return res;
}
void laguange()
{
long long res;
for (int i=0;i<=k+1;++i) S[i]=T[i]=0;
S[0]=1;
for (int i=1;i<=k+1;++i)
{
for (int j=k+1;j>=1;--j) S[j]=(S[j-1]-S[j]*i%mod)%mod;
S[0]=-S[0]*i%mod;
}
for (int i=1;i<=k+1;++i)
{
S[0]=-S[0]*inv[i]%mod,res=1;
for (int j=1;j<=k+1;++j) S[j]=(S[j-1]-S[j])*inv[i]%mod;
for (int j=1;j<=k+1;++j)
{
if (j>i) res=-res*inv[j-i]%mod;
if (i>j) res=res*inv[i-j]%mod;
}
for (int j=0;j<=k;++j) T[j]=(T[j]+S[j]*A[i]%mod*res%mod)%mod;
for (int j=k+1;j>=1;--j) S[j]=(S[j-1]-S[j]*i%mod)%mod;
S[0]=-S[0]*i%mod;
}
return;
}
int solve(int r,int c,int v)
{
r+=max(v-2,0ll),c+=max(v-2,0ll);
long long res=0;
for (int i=1;i<=k;++i)
for (int j=1;j<=k;++j)
s1[i][j]=G(n+(i-1),i-1,j-1,m+(j-1),r-1,c-1),s2[i][j]=(F(n+(i-1),i-1,j-1,m+(j-1))-s1[i][j])%mod;
for (int i=1;i<=k+1;++i) A[i]=gauss(i);
laguange();
for (int i=v-1;i<=k;++i) res=(res+T[i])%mod;
return res;
}
signed main()
{
int r,c,v;
n=read(),m=read(),k=read()-1,r=read(),c=read(),v=read(),C[0][0]=inv[1]=1;
for (int i=2;i<=k+1;++i) inv[i]=inv[mod%i]*(-mod/i)%mod;
for (int i=0;i<=N;++i) C[i][0]=1;
for (int i=1;i<=N;++i)
for (int j=1;j<=i;++j)
C[i][j]=(C[i-1][j]+C[i-1][j-1])%mod;
printf("%lld\n",((solve(r,c,v)-solve(r,c,v+1))%mod+mod)%mod);
return 0;
}
Details
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Test #1:
score: 100
Accepted
time: 36ms
memory: 43264kb
input:
148 129 48 144 105 13
output:
467058311
result:
ok single line: '467058311'
Test #2:
score: 0
Accepted
time: 0ms
memory: 40768kb
input:
57 48 11 56 9 1
output:
951177245
result:
ok single line: '951177245'
Test #3:
score: 0
Accepted
time: 115ms
memory: 42876kb
input:
121 146 72 117 72 25
output:
284798523
result:
ok single line: '284798523'
Test #4:
score: 0
Accepted
time: 4ms
memory: 40932kb
input:
66 142 11 51 124 4
output:
542285716
result:
ok single line: '542285716'
Test #5:
score: 0
Accepted
time: 313ms
memory: 45308kb
input:
45 127 98 3 31 80
output:
116902187
result:
ok single line: '116902187'
Test #6:
score: 0
Accepted
time: 24ms
memory: 40820kb
input:
125 199 45 51 91 21
output:
715355617
result:
ok single line: '715355617'
Test #7:
score: 0
Accepted
time: 3ms
memory: 40680kb
input:
41 153 6 6 147 2
output:
190519561
result:
ok single line: '190519561'
Test #8:
score: 0
Accepted
time: 101ms
memory: 43300kb
input:
112 108 69 99 29 47
output:
481688971
result:
ok single line: '481688971'
Test #9:
score: 0
Accepted
time: 275ms
memory: 43132kb
input:
138 99 94 73 43 73
output:
667469005
result:
ok single line: '667469005'
Test #10:
score: 0
Accepted
time: 4ms
memory: 39164kb
input:
143 147 18 24 141 9
output:
763965115
result:
ok single line: '763965115'
Test #11:
score: 0
Accepted
time: 300ms
memory: 45304kb
input:
99 63 97 78 51 66
output:
130195301
result:
ok single line: '130195301'
Test #12:
score: 0
Accepted
time: 4ms
memory: 41164kb
input:
103 23 10 25 7 4
output:
674555733
result:
ok single line: '674555733'
Test #13:
score: 0
Accepted
time: 22ms
memory: 40716kb
input:
137 194 42 125 104 17
output:
416667361
result:
ok single line: '416667361'
Test #14:
score: 0
Accepted
time: 16ms
memory: 40872kb
input:
191 13 37 42 2 21
output:
530754407
result:
ok single line: '530754407'
Test #15:
score: 0
Accepted
time: 45ms
memory: 40920kb
input:
195 33 53 101 29 32
output:
851306824
result:
ok single line: '851306824'
Test #16:
score: 0
Accepted
time: 4ms
memory: 40924kb
input:
84 173 8 70 70 6
output:
25135799
result:
ok single line: '25135799'
Test #17:
score: 0
Accepted
time: 34ms
memory: 41192kb
input:
39 53 49 37 6 9
output:
640044940
result:
ok single line: '640044940'
Test #18:
score: 0
Accepted
time: 97ms
memory: 44880kb
input:
135 129 68 134 86 16
output:
910022919
result:
ok single line: '910022919'
Test #19:
score: 0
Accepted
time: 53ms
memory: 43188kb
input:
62 74 56 28 12 46
output:
774987233
result:
ok single line: '774987233'
Test #20:
score: 0
Accepted
time: 160ms
memory: 43200kb
input:
87 135 81 27 44 58
output:
629485683
result:
ok single line: '629485683'
Test #21:
score: 0
Accepted
time: 27ms
memory: 41128kb
input:
148 199 44 79 81 40
output:
369408819
result:
ok single line: '369408819'
Test #22:
score: 0
Accepted
time: 0ms
memory: 38848kb
input:
18 195 5 17 151 5
output:
198068951
result:
ok single line: '198068951'
Test #23:
score: 0
Accepted
time: 130ms
memory: 42976kb
input:
200 137 75 67 65 74
output:
864017958
result:
ok single line: '864017958'
Test #24:
score: 0
Accepted
time: 50ms
memory: 42756kb
input:
171 162 56 113 97 30
output:
255341800
result:
ok single line: '255341800'
Test #25:
score: 0
Accepted
time: 15ms
memory: 42776kb
input:
8 134 38 1 93 10
output:
282048962
result:
ok single line: '282048962'
Test #26:
score: 0
Accepted
time: 258ms
memory: 43028kb
input:
13 55 93 3 25 40
output:
852404927
result:
ok single line: '852404927'
Test #27:
score: 0
Accepted
time: 20ms
memory: 40992kb
input:
169 157 42 77 108 39
output:
595819517
result:
ok single line: '595819517'
Test #28:
score: 0
Accepted
time: 208ms
memory: 45336kb
input:
41 199 87 18 82 58
output:
698977796
result:
ok single line: '698977796'
Test #29:
score: 0
Accepted
time: 54ms
memory: 42844kb
input:
190 68 57 188 59 15
output:
46174623
result:
ok single line: '46174623'
Test #30:
score: 0
Accepted
time: 109ms
memory: 44852kb
input:
90 52 71 39 41 23
output:
417181087
result:
ok single line: '417181087'
Test #31:
score: 0
Accepted
time: 228ms
memory: 42904kb
input:
108 76 89 55 40 13
output:
210578964
result:
ok single line: '210578964'
Test #32:
score: 0
Accepted
time: 9ms
memory: 40784kb
input:
166 191 27 102 30 11
output:
365224233
result:
ok single line: '365224233'
Test #33:
score: 0
Accepted
time: 3ms
memory: 40828kb
input:
41 166 4 10 49 2
output:
245797147
result:
ok single line: '245797147'
Test #34:
score: 0
Accepted
time: 149ms
memory: 45460kb
input:
135 128 79 44 16 6
output:
203896980
result:
ok single line: '203896980'
Test #35:
score: 0
Accepted
time: 157ms
memory: 43180kb
input:
101 193 79 43 65 75
output:
27637457
result:
ok single line: '27637457'
Test #36:
score: 0
Accepted
time: 37ms
memory: 40932kb
input:
88 81 53 35 54 47
output:
950708598
result:
ok single line: '950708598'
Test #37:
score: 0
Accepted
time: 6ms
memory: 38996kb
input:
87 40 28 37 8 8
output:
817953396
result:
ok single line: '817953396'
Test #38:
score: 0
Accepted
time: 275ms
memory: 45380kb
input:
193 136 94 12 94 23
output:
145619900
result:
ok single line: '145619900'
Test #39:
score: 0
Accepted
time: 91ms
memory: 42840kb
input:
90 183 67 8 171 26
output:
899333159
result:
ok single line: '899333159'
Test #40:
score: 0
Accepted
time: 12ms
memory: 41068kb
input:
107 178 32 24 103 12
output:
82019799
result:
ok single line: '82019799'
Test #41:
score: 0
Accepted
time: 67ms
memory: 42900kb
input:
160 23 61 60 17 3
output:
350971684
result:
ok single line: '350971684'
Test #42:
score: 0
Accepted
time: 4ms
memory: 39188kb
input:
100 176 10 54 58 4
output:
978823166
result:
ok single line: '978823166'
Test #43:
score: 0
Accepted
time: 22ms
memory: 40960kb
input:
181 183 42 7 91 41
output:
690262327
result:
ok single line: '690262327'
Test #44:
score: 0
Accepted
time: 28ms
memory: 41000kb
input:
105 131 47 53 68 33
output:
806603020
result:
ok single line: '806603020'
Test #45:
score: 0
Accepted
time: 330ms
memory: 46916kb
input:
51 10 100 1 5 73
output:
341852925
result:
ok single line: '341852925'
Test #46:
score: 0
Accepted
time: 118ms
memory: 43224kb
input:
87 198 73 75 109 72
output:
741170008
result:
ok single line: '741170008'
Test #47:
score: 0
Accepted
time: 4ms
memory: 40824kb
input:
25 158 13 22 1 1
output:
237363061
result:
ok single line: '237363061'
Test #48:
score: 0
Accepted
time: 109ms
memory: 44844kb
input:
64 112 71 28 109 10
output:
350168232
result:
ok single line: '350168232'
Test #49:
score: 0
Accepted
time: 42ms
memory: 43044kb
input:
143 191 52 10 98 10
output:
71885894
result:
ok single line: '71885894'
Test #50:
score: 0
Accepted
time: 14ms
memory: 41296kb
input:
30 130 36 22 85 6
output:
909971212
result:
ok single line: '909971212'
Test #51:
score: 0
Accepted
time: 16ms
memory: 40952kb
input:
154 136 38 34 109 15
output:
655764791
result:
ok single line: '655764791'
Test #52:
score: 0
Accepted
time: 3ms
memory: 38968kb
input:
13 112 7 9 55 1
output:
623849663
result:
ok single line: '623849663'
Test #53:
score: 0
Accepted
time: 25ms
memory: 40888kb
input:
137 103 47 56 77 35
output:
43033659
result:
ok single line: '43033659'
Test #54:
score: 0
Accepted
time: 15ms
memory: 41324kb
input:
40 17 37 11 7 15
output:
803046927
result:
ok single line: '803046927'
Test #55:
score: 0
Accepted
time: 56ms
memory: 41332kb
input:
166 14 58 49 1 26
output:
664593299
result:
ok single line: '664593299'
Test #56:
score: 0
Accepted
time: 4ms
memory: 40760kb
input:
88 195 15 10 120 5
output:
925522664
result:
ok single line: '925522664'
Test #57:
score: 0
Accepted
time: 291ms
memory: 44816kb
input:
164 166 96 161 138 32
output:
111053370
result:
ok single line: '111053370'
Test #58:
score: 0
Accepted
time: 270ms
memory: 44884kb
input:
145 135 94 68 83 9
output:
394110532
result:
ok single line: '394110532'
Test #59:
score: 0
Accepted
time: 70ms
memory: 41004kb
input:
154 173 63 5 77 51
output:
540440686
result:
ok single line: '540440686'
Test #60:
score: 0
Accepted
time: 7ms
memory: 41264kb
input:
20 91 30 20 83 17
output:
961395776
result:
ok single line: '961395776'
Test #61:
score: 0
Accepted
time: 3ms
memory: 39300kb
input:
144 39 13 77 9 5
output:
99731481
result:
ok single line: '99731481'
Test #62:
score: 0
Accepted
time: 176ms
memory: 43076kb
input:
87 152 83 4 59 81
output:
139490896
result:
ok single line: '139490896'
Test #63:
score: 0
Accepted
time: 224ms
memory: 43060kb
input:
171 135 89 114 124 10
output:
736020363
result:
ok single line: '736020363'
Test #64:
score: 0
Accepted
time: 320ms
memory: 43216kb
input:
82 41 99 66 6 5
output:
882042301
result:
ok single line: '882042301'
Test #65:
score: 0
Accepted
time: 7ms
memory: 41004kb
input:
33 114 28 11 73 11
output:
653378940
result:
ok single line: '653378940'
Test #66:
score: 0
Accepted
time: 0ms
memory: 39148kb
input:
180 73 10 43 63 9
output:
170492767
result:
ok single line: '170492767'
Test #67:
score: 0
Accepted
time: 71ms
memory: 42880kb
input:
33 185 63 19 107 7
output:
907253908
result:
ok single line: '907253908'
Test #68:
score: 0
Accepted
time: 7ms
memory: 39148kb
input:
69 90 22 34 31 3
output:
137223161
result:
ok single line: '137223161'
Test #69:
score: 0
Accepted
time: 60ms
memory: 40988kb
input:
42 45 60 29 38 36
output:
99908563
result:
ok single line: '99908563'
Test #70:
score: 0
Accepted
time: 13ms
memory: 40780kb
input:
69 158 34 56 39 17
output:
681472254
result:
ok single line: '681472254'
Test #71:
score: 0
Accepted
time: 188ms
memory: 45428kb
input:
66 69 84 5 8 41
output:
277373736
result:
ok single line: '277373736'
Test #72:
score: 0
Accepted
time: 95ms
memory: 40916kb
input:
168 31 68 66 4 21
output:
528816013
result:
ok single line: '528816013'
Test #73:
score: 0
Accepted
time: 272ms
memory: 42948kb
input:
65 33 94 2 30 76
output:
331224077
result:
ok single line: '331224077'
Test #74:
score: 0
Accepted
time: 4ms
memory: 41248kb
input:
84 111 12 28 106 12
output:
95279945
result:
ok single line: '95279945'
Test #75:
score: 0
Accepted
time: 183ms
memory: 43184kb
input:
102 77 83 95 62 51
output:
773914979
result:
ok single line: '773914979'
Test #76:
score: 0
Accepted
time: 132ms
memory: 43368kb
input:
113 144 76 24 68 13
output:
845242590
result:
ok single line: '845242590'
Test #77:
score: 0
Accepted
time: 0ms
memory: 41280kb
input:
45 24 9 10 2 5
output:
71790514
result:
ok single line: '71790514'
Test #78:
score: 0
Accepted
time: 68ms
memory: 43280kb
input:
158 98 61 86 50 29
output:
123475901
result:
ok single line: '123475901'
Test #79:
score: 0
Accepted
time: 8ms
memory: 40916kb
input:
118 52 27 11 23 21
output:
489202572
result:
ok single line: '489202572'
Test #80:
score: 0
Accepted
time: 15ms
memory: 40928kb
input:
122 148 35 112 17 17
output:
856169627
result:
ok single line: '856169627'
Test #81:
score: 0
Accepted
time: 0ms
memory: 39200kb
input:
135 114 15 20 43 9
output:
873320383
result:
ok single line: '873320383'
Test #82:
score: 0
Accepted
time: 189ms
memory: 44896kb
input:
89 70 84 70 12 18
output:
302990320
result:
ok single line: '302990320'
Test #83:
score: 0
Accepted
time: 90ms
memory: 42864kb
input:
15 68 67 5 51 66
output:
980298686
result:
ok single line: '980298686'
Test #84:
score: 0
Accepted
time: 119ms
memory: 42784kb
input:
50 2 73 40 2 8
output:
550497760
result:
ok single line: '550497760'
Test #85:
score: 0
Accepted
time: 179ms
memory: 43288kb
input:
117 88 83 93 1 50
output:
645491986
result:
ok single line: '645491986'
Test #86:
score: 0
Accepted
time: 47ms
memory: 40972kb
input:
45 173 54 34 93 3
output:
330947509
result:
ok single line: '330947509'
Test #87:
score: 0
Accepted
time: 5ms
memory: 38904kb
input:
39 10 22 34 6 20
output:
184357429
result:
ok single line: '184357429'
Test #88:
score: 0
Accepted
time: 101ms
memory: 43204kb
input:
58 27 71 55 19 22
output:
201813851
result:
ok single line: '201813851'
Test #89:
score: 0
Accepted
time: 17ms
memory: 41096kb
input:
123 57 40 14 38 23
output:
891805630
result:
ok single line: '891805630'
Test #90:
score: 0
Accepted
time: 103ms
memory: 43116kb
input:
84 64 70 12 2 23
output:
351372969
result:
ok single line: '351372969'
Test #91:
score: 0
Accepted
time: 114ms
memory: 43332kb
input:
46 160 72 21 146 9
output:
625614461
result:
ok single line: '625614461'
Test #92:
score: 0
Accepted
time: 50ms
memory: 43172kb
input:
45 99 57 25 40 4
output:
498175745
result:
ok single line: '498175745'
Test #93:
score: 0
Accepted
time: 4ms
memory: 40840kb
input:
15 21 12 14 6 3
output:
727195216
result:
ok single line: '727195216'
Test #94:
score: 0
Accepted
time: 11ms
memory: 41036kb
input:
154 77 32 73 62 15
output:
513610382
result:
ok single line: '513610382'
Test #95:
score: 0
Accepted
time: 6ms
memory: 38928kb
input:
165 97 16 158 69 11
output:
308621770
result:
ok single line: '308621770'
Test #96:
score: 0
Accepted
time: 308ms
memory: 43132kb
input:
146 128 97 132 24 10
output:
751957330
result:
ok single line: '751957330'
Test #97:
score: 0
Accepted
time: 15ms
memory: 40720kb
input:
49 39 35 2 10 14
output:
338882448
result:
ok single line: '338882448'
Test #98:
score: 0
Accepted
time: 120ms
memory: 42776kb
input:
73 1 73 35 1 44
output:
126891463
result:
ok single line: '126891463'
Test #99:
score: 0
Accepted
time: 60ms
memory: 40908kb
input:
69 82 59 1 73 1
output:
436743471
result:
ok single line: '436743471'
Test #100:
score: 0
Accepted
time: 16ms
memory: 40980kb
input:
88 86 40 19 77 4
output:
758000538
result:
ok single line: '758000538'